Simple Equations Worksheet

Fill in the blanks Type Questions

1. Anya wants a new watch on her birthday and so she looks for some watches online. While doing an online shopping, she found ‘x’ number of watches matching the filters applied by her. When she removes the filter, the total number of watches visible to her is 63 less than thrice the number of watches visible after applying the filter. If total 273 watches are visible, then the value of x is __________.
2. While playing a game of chess, Manish counts the number of boxes on the chessboard that have no chess pieces. 
   
   
   He then constructs an equation “x + 25 = 64” where ‘x’ is the number of boxes with no chess pieces. The first step to separate the variable is “___________________” and so we get the value of x as 39.
3. Sheetal and Divya are best friends. But on one day, Divya was not well so she didn’t come to school. On that day, Sheetal was returning all alone from the school and so she thought of counting the number of footsteps required to reach the bus stop.
    
   She formed an equation which is “2m – 32 = 140” where m is the number of steps required to reach the bus stop. So, the value of m will be _________.
4. Amita invited 80 people for a Christmas party organised at his house and wrapped 90 gifts keeping 10 extra on a side.
    
   Now after the party, he distributed return gifts one to each individual and then the guests left. If “2x – 4 = 80” is true where ‘x’ is the number of people who attended the party, then x = 42 is the __________ of the above equation.
5. On Sports day, 56 students participated only in Long Jump, ‘m’ students participated only in race and number of students participated only in Jawelin throw is twice the number of students participated only in race. 
   
   If the total number of students participated in any of the three sports is 180, the equation formed is given by _______________.
6. There are ‘m’ chairs and ‘n’ tables arranged in the Flower Café shop near Celin’s house. 
   
   The number of chairs depends on the number of tables and it is given by the equation 2m – n = 8. The statement form for this equation is “twice the number of chairs is equal to _____________________ the number of tables”.
   
   Multiple Choice Questions
   
   
7. During school vacation of 30 days, Ridhima has to write 250 pages as instructed by her teacher. She writes x pages on the first day. In the next 29 days, she has to write y pages every day to complete the homework. How will you express this situation?
   (a)x + y = 250
   (b)x + 29y = 250
   (c)29x + y = 250
   (d)29x – y = 250
8. Keshav bought 10 kg of grains to feed pigeons. He feeds x kg of grains in the first one hour.
   
   Remaining y kg of grains are distributed so that he feeds ½ kg every hour. Then this situation can be represented as ______________________.
   (a) x + ½ y = 10
   (b) ½ x + y = 10
   (c) x – ½ y = 10
   (d) x + y = 10
   
   
9. Anwi’s friends visit her house during summer vacation, so she makes lemon juice for them. She distribute x glasses of juice to the friends (one glass to each one) sitting on the left side and remaining y glasses of juice to the friends (one glass to each one) sitting on the right side. If there are 21 people in the room, what are the possible values of x and y?
   
   
   (a) x = 8, y = 2
   (b) x = 12, y = 7
   (c) x = 11, y = 9
   (d) x = 5, y = 14
10. Rohit has x number of shirts and his sister Raveena has y number of dresses. Then which of the following statement gives the correct explanation for the equation “y – 2x = 4”?
    (a) The number of shirts Rohit has is equal to 4 more than the number of dresses Raveena has.
    (b) The number of shirts Rohit has is equal to 4 less than twice the number of dresses Raveena has.
    (c) The number of dresses Raveena has is equal to 4 more than twice the number of shirts Rohit has.
    (d) The number of dresses Raveena has is equal to 4 less than the number of shirts Rohit has.
11. There are ‘m’ number of sling bags and ‘n’ number of hand bags in a shopping centre.
     
    If m + 2n = 400, which of the following statement is correct?
    (a) Number of sling bags and twice the number of hand bags is collectively 400.
    (b) Number of sling bags is 400 less than twice the number of hand bags.
    (c) Number of hand bags and the number of sling bags is collectively 400.
    (d) Number of hand bags is 400 less than the number of sling bags.
12. Raunak went to a National park twice and listed down the number of domestic animals and wild animals he saw every time.
     
    Let ‘x’ represents domestic animals and ‘y’ represents wild animals. Total number of animals in the 1st time is “x + 2y” and in the 2nd time is “2x + y + 10”. If the total number of animals remains the same for both the times, find the simplified equation.
    (a) x + y = 10
    (b) x – y = 10
    (c) x + 2y = 10
    (d) y – x = 10
13. Dhanush runs flower shop having ‘x’ number of flower bouquets.
     
    He brings 10 such flower bouquets each having ‘y’ number of flowers in it for the party organised by him. When we subtract 4 from the total number of flowers, the number we obtain is 46. What is the value of y?
    (a) 4
    (b) 46/10
    (c) 5
    (d) 52/10
14. Mangoes play a vital role in boosting our immunity during summer season as it is a storehouse of innumerable nutrients. So, Ravi bought ‘x’ boxes of mangoes and then 2 more boxes each for Rs. 1050 which gives a total of Rs. 7350.
     
    How many boxes of mangoes did he buy in total?
    (a) 3
    (b) 5
    (c) 7
    (d) 1
    
    Subjective Questions
    
    
15. Arya’s father is preparing for KBC and so he studies few general knowledge books. Arya took one of the books and read that the world’s tallest building has 163 floors in it. She imagine and divide the floors of this building so that “x + 2y = 163”. If she claims that 109 & 27 will replace x and y respectively, is Arya correct? Justify your answer.
16. Sanju used few paper tea cups to make wall hangings and ceiling hangings as given below:
    
    He made ‘x’ such ceiling hangings and ‘2x’ such wall hangings. If the number of cups used for ceiling hangings is 20 more than the number of cups used for wall hangings. Write the simplified equation (variables on one side).
17. There are total ‘x’ different types of fishes in an aquarium and 2 fishes of each type are present in it. When you take twice the total number of fishes and add fifty and then take out 30, you get hundred more than two hundred. Find the total number of fishes present in the aquarium.
18. In a cricket match, MS Dhoni scored some singles, some 4s and some 6s. His total score was 96 with ‘x’ singles, 8 fours and 6 sixes. If he played 47 balls, how many were dot balls?
    
    
    
19. Arun bought a story book having 240 pages in it. He finished reading 23 pages on the first day. From 2nd day, he use to read 31 pages every day and finished reading the entire book in ‘x’ days.
    
    An equation formed with the above information is “23 + 31x = 240”. Show the step to separate the variable and then find the number of days required to finish reading the entire book.
20. While doing a math trick, Trisha takes a number and doubles it. She then takes away half of 18 from it and divide it by 7 to get the 3rd multiple of 17. Find the number took by Trisha.
    
    

Fill in the blanks Type Questions

1. Anya wants a new watch on her birthday and so she looks for some watches online. While doing an online shopping, she found ‘x’ number of watches matching the filters applied by her. When she removes the filter, the total number of watches visible to her is 63 less than thrice the number of watches visible after applying the filter. If total 273 watches are visible, then the value of x is __________.
   Correct Answer: 112
   Solution:
   Total number of watches = 273
   ∴ 3x – 63 = 273
   ∴ 3x = 336
   ∴ x = 112
2. While playing a game of chess, Manish counts the number of boxes on the chessboard that have no chess pieces. 
   
   
   He then constructs an equation “x + 25 = 64” where ‘x’ is the number of boxes with no chess pieces. The first step to separate the variable is “___________________” and so we get the value of x as 39.
   Correct Answer: subtract 25 from both the sides
   Solution:
   Equation constructed by Manish is:
   x + 25 = 64
   The first step to separate the variable is “subtract 25 from both the sides”.
   ∴ x + 25 – 25 = 64 – 25
   ∴ x = 39
3. Sheetal and Divya are best friends. But on one day, Divya was not well so she didn’t come to school. On that day, Sheetal was returning all alone from the school and so she thought of counting the number of footsteps required to reach the bus stop.
    
   She formed an equation which is “2m – 32 = 140” where m is the number of steps required to reach the bus stop. So, the value of m will be _________.
   Correct Answer: 86
   Solution:
   Equation formed by Sheetal is:
   2m – 32 = 140
   Add 32 on both the sides
   ∴ 2m – 32 + 32 = 140 + 32
   ∴ 2m = 172
   Divide both sides by 2
   ∴ m = 86
   So, the value of m will be 86.
4. Amita invited 80 people for a Christmas party organised at his house and wrapped 90 gifts keeping 10 extra on a side.
    
   Now after the party, he distributed return gifts one to each individual and then the guests left. If “2x – 4 = 80” is true where ‘x’ is the number of people who attended the party, then x = 42 is the __________ of the above equation.
   Correct Answer: Solution
   Solution:
   As 2x – 4 = 80
   Take x = 42
   ∴ 2x – 4 = 2 × 42 – 4 = 84 – 4 = 80
   So, x = 42 is the solution of the above equation.
5. On Sports day, 56 students participated only in Long Jump, ‘m’ students participated only in race and number of students participated only in Jawelin throw is twice the number of students participated only in race. 
   
   If the total number of students participated in any of the three sports is 180, the equation formed is given by _______________.
   Correct Answer: 56 + 3m = 180
   Solution:
   Total number of students participated in any of the three sports = 180
   Also, total number of students participated in any of the three sports = 56 + m + 2m = 56 + 3m
   ∴ 56 + 3m = 180
   So, if the total number of students participated in any of the three sports is 180, the equation formed is given by 56 + 3m = 180.
6. There are ‘m’ chairs and ‘n’ tables arranged in the Flower Café shop near Celin’s house. 
   
   The number of chairs depends on the number of tables and it is given by the equation 2m – n = 8. The statement form for this equation is “twice the number of chairs is equal to _____________________ the number of tables”.
   Correct Answer: 8 more than
   Solution:
   The equation given is:
   2m – n = 8
   Add ‘n’ to both the sides
   ∴ 2m = 8 + n
   So, twice the number of chairs is equal to 8 more than the number of tables.
   
   Multiple Choice Questions
   
   
7. During school vacation of 30 days, Ridhima has to write 250 pages as instructed by her teacher. She writes x pages on the first day. In the next 29 days, she has to write y pages every day to complete the homework. How will you express this situation?
   (a) x + y = 250
   (b) x + 29y = 250
   (c) 29x + y = 250
   (d) 29x – y = 250
   Correct Option: (b) x + 29y = 250
   Solution:
   In the next 29 days, Ridhima write y pages every day.
   So, she will finish writing 29y pages in 29 days.
   And, she write x pages on the 1st day.
   ∴ x + 29y = 250
8. Keshav bought 10 kg of grains to feed pigeons. He feeds x kg of grains in the first one hour.
   
   Remaining y kg of grains are distributed so that he feeds ½ kg every hour. Then this situation can be represented as ______________________.
   (a) x + ½ y = 10
   (b) ½ x + y = 10
   (c) x – ½ y = 10
   (d) x + y = 10
   Correct Option: (d) x + y = 10
   Solution:
   In one hour, Keshav feeds x kg of grains to the pigeons.
   He then feeds ½ kg grains every hour and finishes remaining y kg of grains.
   So, this situation can be represented as x + y = 10.
9. Anwi’s friends visit her house during summer vacation, so she makes lemon juice for them. She distribute x glasses of juice to the friends (one glass to each one) sitting on the left side and remaining y glasses of juice to the friends (one glass to each one) sitting on the right side. If there are 21 people in the room, what are the possible values of x and y?
   
   
   (a) x = 8, y = 2
   (b) x = 12, y = 7
   (c) x = 11, y = 9
   (d) x = 5, y = 14
   Correct Option: (c) x = 11, y = 9
   Solution:
   There are x friends on the left side and y friends on the right side of Anwi.
   ∴ Number of people in the room = x + y + 1
   ∴ x + y + 1 = 21
   ∴ x + y = 20
   But, 11 + 9 = 20
   So, the possible values of x and y are x = 11 and y = 9.
10. Rohit has x number of shirts and his sister Raveena has y number of dresses. Then which of the following statement gives the correct explanation for the equation “y – 2x = 4”?
    (a) The number of shirts Rohit has is equal to 4 more than the number of dresses Raveena has.
    (b) The number of shirts Rohit has is equal to 4 less than twice the number of dresses Raveena has.
    (c) The number of dresses Raveena has is equal to 4 more than twice the number of shirts Rohit has.
    (d) The number of dresses Raveena has is equal to 4 less than the number of shirts Rohit has.
    Correct Option: (c) The number of dresses Raveena has is equal to 4 more than twice the number of shirts Rohit has.
    Solution:
    It is given that, y – 2x = 4
    ∴ y = 2x + 4
    Here, 2x represents “twice the number of shirts”.
    So, the statement that well explains the above equation is:
    “The number of dresses Raveena has is 4 more than twice the number of shirts Rohit has”.
11. There are ‘m’ number of sling bags and ‘n’ number of hand bags in a shopping centre.
     
    If m + 2n = 400, which of the following statement is correct?
    (a) Number of sling bags and twice the number of hand bags is collectively 400.
    (b) Number of sling bags is 400 less than twice the number of hand bags.
    (c) Number of hand bags and the number of sling bags is collectively 400.
    (d) Number of hand bags is 400 less than the number of sling bags.
    Correct Option: (a) Number of sling bags and twice the number of hand bags is collectively 400.
    Solution:
    Given: m + 2n = 400
    Clearly, the sum of the number of sling bags and the number of hand bags is 400.
12. Raunak went to a National park twice and listed down the number of domestic animals and wild animals he saw every time.
     
    Let ‘x’ represents domestic animals and ‘y’ represents wild animals. Total number of animals in the 1st time is “x + 2y” and in the 2nd time is “2x + y + 10”. If the total number of animals remains the same for both the times, find the simplified equation.
    (a) x + y = 10
    (b) x – y = 10
    (c) x + 2y = 10
    (d) y – x = 10
    Correct Option: (d) y – x = 10
    Solution:
    Here, total number of animals in the 1st time = x + 2y.
    And, total number of animals in the 2nd time = 2x + y + 10.
    Since, the total number of animals remains the same for both the times.
    ∴ x + 2y = 2x + y + 10
    Bring variables on the LHS, we get
    x + 2y – 2x – y = 10
    y – x = 10
13. Dhanush runs flower shop having ‘x’ number of flower bouquets.
     
    He brings 10 such flower bouquets each having ‘y’ number of flowers in it for the party organised by him. When we subtract 4 from the total number of flowers, the number we obtain is 46. What is the value of y?
    (a) 4
    (b) 46/10
    (c) 5
    (d) 52/10
    Correct Option: (c) 5
    Solution:
    Total number of flowers brought by Dhanush for the party = 10y
    Subtracting 4 from it will give us 46
    ∴ 10y – 4 = 46
    ∴ 10y = 46 + 4
    ∴ 10y = 50
    ∴ y = 5
14. Mangoes play a vital role in boosting our immunity during summer season as it is a storehouse of innumerable nutrients. So, Ravi bought ‘x’ boxes of mangoes and then 2 more boxes each for Rs. 1050 which gives a total of Rs. 7350.
     
    How many boxes of mangoes did he buy in total?
    (a) 3
    (b) 5
    (c) 7
    (d) 1
    Correct Option: (c) 7
    Solution:
    Each box costs Rs. 1050.
    ∴ 1050 × x + 1050 × 2 = 7350
    ∴ 1050x + 2100 = 7350
    ∴ 1050x = 7350 – 2100
    ∴ 1050x = 5250
    ∴ x = 5
    ∴ x + 2 = 7
    So, Ravi bought total 7 boxes of mangoes.
    
    Subjective Questions
    
    
15. Arya’s father is preparing for KBC and so he studies few general knowledge books. Arya took one of the books and read that the world’s tallest building has 163 floors in it. She imagine and divide the floors of this building so that “x + 2y = 163”. If she claims that 109 & 27 will replace x and y respectively, is Arya correct? Justify your answer.
    Solution:
    By using hit and trial method, put x = 109 and y = 27
    109 + 2×27 = 109 + 54 = 163
    So, x + 2y = 163 is true for x = 109 and y = 27.
    Thus, Arya is correct
16. Sanju used few paper tea cups to make wall hangings and ceiling hangings as given below:
    
    He made ‘x’ such ceiling hangings and ‘2x’ such wall hangings. If the number of cups used for ceiling hangings is 20 more than the number of cups used for wall hangings. Write the simplified equation (variables on one side).
    Solution:
    13x = 5(2x) + 20
    13x = 10x + 20
    Bring 10x to the LHS
    13x – 10x = 20
    3x = 20
17. There are total ‘x’ different types of fishes in an aquarium and 2 fishes of each type are present in it. When you take twice the total number of fishes and add fifty and then take out 30, you get hundred more than two hundred. Find the total number of fishes present in the aquarium.
    Solution:
    Types of fishes in the aquarium = x
    As there are 2 fishes of each type present in the aquarium.
    So, the total number of fishes = 2x
    Now, twice the total number of fishes = 2 × (2x)
    As per the condition given, we have
    ∴ 2 × (2x) + 50 – 30 = 200 + 100
    ∴ 4x + 20 = 300
    ∴ 4x = 300 – 20
    ∴ 4x = 280
    Dividing throughout by 4
    ∴ x = 70
18. In a cricket match, MS Dhoni scored some singles, some 4s and some 6s. His total score was 96 with ‘x’ singles, 8 fours and 6 sixes. If he played 47 balls, how many were dot balls?
    
    
    Solution:
    Total score = 96
    ∴ x + 8×4 + 6×6 = 96
    ∴ x + 32 + 36 = 96
    ∴ x + 68 = 96
    ∴ x = 96 – 68
    ∴ x = 28
    He played 47 balls.
    28 singles will require 28 balls, 8 fours need 8 balls and 6 sixes need 6 balls.
    Now, 28 + 8 + 6 = 42
    But 47 – 42 = 5
    So, there were 5 dot balls.
    
    
19. Arun bought a story book having 240 pages in it. He finished reading 23 pages on the first day. From 2nd day, he use to read 31 pages every day and finished reading the entire book in ‘x’ days.
    
    An equation formed with the above information is “23 + 31x = 240”. Show the step to separate the variable and then find the number of days required to finish reading the entire book.
    Solution:
    Equation formed is:
    23 + 31x = 240
    To separate variable, subtract 23 from both the sides.
    ∴ 23 + 31x – 23 = 240 – 23
    ∴ 31x = 217
    Dividing both the sides by 31
    ∴ x = 7
    As Arun finished reading 23 pages on the first day and rest of the pages in ‘x’ days.
    So, he will require 8 days to finish reading the entire book.
20. While doing a math trick, Trisha takes a number and doubles it. She then takes away half of 18 from it and divide it by 7 to get the 3rd multiple of 17. Find the number took by Trisha.
    
    
    Solution:
    Let Trisha takes a number ‘x’.
    Double of it is ‘2x’.
    Since, half of 18 is 9.
    Taking 9 from 2x is ‘2x – 9’.
    Now, 3rd multiple of 17 is 51.
    ∴ (2x-9)/7=51
    ∴ 2x – 9 = 51 × 7
    ∴ 2x – 9 = 357
    Adding 9 on both the sides
    ∴ 2x – 9 + 9 = 357 + 9
    ∴ 2x = 366
    Dividing both sides by 2
    ∴ x = 183
    So, the number took by Trisha is 183.