Applications of Linear Equations-Gr 7-Solved Examples

Solved Examples and Worksheet for Applications of Linear Equations

Q1There are 4 classrooms in a school each having the same number of students. How many students are in each class if 148 attend at that school ?

A. 38
B. 37
C. 42
D. 32

Solutions

Step: 1

Let n be the strength of the each classroom.

Step: 2

4n = 148

[Write an equation.]

Step: 3

4n4 = 1484

[Divide each side by 4.]

Step: 4

n = 37

[Simplify.]

Step: 5

So, the strength of each classroom is 37.

Correct Answer is : 37

Q2Josh bought 7 books for $66.22. What is the cost of each book, if each of them costs the same?
A. $10.46
B. $9.46
C. $8.46
D. $9.96

Solutions

Step: 1

Let n be the cost of each book.

Step: 2

7n = 66.22

[Write an equation.]

Step: 3

7n7 = 66.227

[Divide each side by 7.]

Step: 4

n = 9.46

[Simplify.]

Step: 5

The cost of each book is $9.46.

Correct Answer is : $9.46

Q3Frank and Brad collected 1003 stamps together. How many stamps did Brad collect, if Frank collected 67 stamps more than Brad did?

A. 401
B. 535
C. 478
D. 468

Solutions

Step: 1

Let n be the number of stamps collected by Brad.

Step: 2

So, the number of stamps collected by Frank = n + 67.

Step: 3

⇒ n + (n + 67) = 1003

[Write the equation for the total number of stamps collected by them.]

Step: 4

⇒ 2n + 67 = 1003

[Combine like terms.]

Step: 5

⇒ 2n = 936

[Subtract 67 from each side.]

Step: 6

⇒ n = 468

[Divide each side by 2.]

Step: 7

Therefore, Brad collected 468 stamps.

Correct Answer is : 468

Q4A farmer wants to fence his field by placing a pole at every 4 feet. How many poles are needed, if the perimeter of the field is 220 feet?
A. 50
B. 55
C. 53
D. 58

Solutions

Step: 1

Let x be the number of poles needed to fence the field.

Step: 2

x = 2204

[Write an equation.]

Step: 3

x = 55

[Simplify.]

Step: 4

55 poles are needed to fence the field.

Correct Answer is : 55

Q5Brian rented a DVD from a video store. The store charges $5 for the first day, and an additional charge of $4 per day from the second day onwards. Brian paid $33 while returning the DVD. Solve the equation 5 + 4n = 33 to find n, the extra number of days that Brian kept the DVD with him.

A. 9
B. 7
C. 6
D. 8

Solutions

Step: 1

5 + 4n = 33

[Original equation.]

Step: 2

5 + 4n - 5 = 33 - 5

[Subtract 5 from each side.]

Step: 3

4n = 28

[Combine like terms.]

Step: 4

4n4 = 284

[Divide each side by 4.]

Step: 5

n = 7

[Simplify.]

Step: 6

Brian kept the DVD for 7 extra days.

Correct Answer is : 7

Q6Find the number of shelves required to place 280 glasses, if each shelf can hold 7 glasses.

A. 40
B. 50
C. 35
D. 47

Solutions

Step: 1

Let n be the number of shelves required to place 280 glasses.

Step: 2

n x 7 = 280

[Original equation.]

Step: 3

n x 77 = 2807

[Divide each side by 7.]

Step: 4

n = 40

[Simplify.]

Step: 5

40 shelves are needed to place 280 glasses.

Correct Answer is : 40

Q7How many racks will be needed to arrange 720 books, if each rack can hold 36 books?

A. 20
B. 22
C. 21
D. 19

Solutions

Step: 1

Let n be the number of racks required to place 36 books.

Step: 2

n × 36 = 720

[Original equation.]

Step: 3

n × 3636 = 72036

[Divide each side by 36.]

Step: 4

n = 20

[Simplify.]

Step: 5

So, 20 racks are required to arrange 720 books.

Correct Answer is : 20

Q8Charles charges $5 for painting a box. How much did he earn, if he painted 49 boxes on a particular day?
A. $245
B. $54
C. $257
D. $490

Solutions

Step: 1

Let n be the amount earned by painting 49 boxes.

Step: 2

Amount earned = (cost of painting each box) x (number of boxes painted)

n = 5 x 49

[Substitute the values.]

Step: 3

n = 245

[Multiply.]

Step: 4

Charles earned $245 on that day.

Correct Answer is : $245

Q9Three people together earn $1110 by doing a piece of work. How much does each person receive, if the amount is distributed equally?
A. $365
B. $374
C. $380
D. $370

Solutions

Step: 1

Let n be the amount received by each person.

Step: 2

Three people together earn $1110.

Step: 3

n = 11103

[Original equation.]

Step: 4

n = 370

[Simplify.]

Step: 5

Each person receives $370.

Correct Answer is : $370

Q10At a grocery store,360 pears are arranged in two boxes P and Q. How many pears does box Q have, if box Q can hold twice as much as what box P can hold?
A. 240
B. 360
C. 120
D. 270

Solutions

Step: 1

Let n be the number of pears in the box P.

Step: 2

Number of pears in the box Q = 2n

Step: 3

n + 2n = 360

[Original equation.]

Step: 4

3n = 360

[Add.]

Step: 5

3n3 = 3603

[Divide each side by 3.]

Step: 6

n = 120

[Simplify.]

Step: 7

2n = 2 × 120 = 240

[Multiply.]

Step: 8

The box Q has 240 pears.

Correct Answer is : 240

Q11The population of City-A is 2 times that of City-B. Find the population of City-A, if the population of City-B is 34445.
A. 68890
B. 68390
C. 80890
D. 178890

Solutions

Step: 1

Let n be the population of City-A.

Step: 2

n = 2 x 34445

[Original equation.]

Step: 3

= 68890

[Multiply.]

Step: 4

The population of City-A is 68890.

Correct Answer is : 68890

Q12George had 102 chocolates. He kept 34 chocolates aside and distributed the rest of the chocolates equally among 2 of his friends. How many chocolates did each of his friends receive?

A. 29
B. 68
C. 34
D. 47

Solutions

Step: 1

Let n be the number of chocolates each friend received.

Step: 2

102 = 2 × n + 34

[Original equation.]

Step: 3

68 = 2 × n

[Subtract 34 from each side.]

Step: 4

n = 34

[Divide each side by 2.]

Step: 5

So, each of his friends received 34 chocolates.

Correct Answer is : 34

Q1327 teams participated in a tournament. Each team played with all the other teams only once. Find the total number of games played by using the equation n(n-1)2, where n represents the total number of teams participated.

A. 351
B. 346
C. 348
D. None of the above

Solutions

Step: 1

n(n-1)2

[Given equation.]

Step: 2

= 27x(27-1)2

[Substitute.]

Step: 3

= 7022

[Simplify.]

Step: 4

= 351

[Divide.]

Step: 5

Total number of games played = 351

Correct Answer is : 351

Q14A family of 6 members went to a movie and spent $48 on tickets. The ticket for an adult costs $12 and that for a child costs $6. How many adults and how many children were there in the family?

A. 2, 4
B. 1, 5
C. 0, 6
D. 3, 3

Solutions

Step: 1

Let n be the number of adults.

Step: 2

Number of children = 6 - n

Step: 3

12n + 6(6 - n) = 48

[Original equation.]

Step: 4

12n + 36 - 6n = 48

[Simplify.]

Step: 5

12n + 36 - 6n - 36 = 48 - 36

[Subtract 36 from each side.]

Step: 6

6n = 12

[Simplify.]

Step: 7

6n6 = 126

[Divide each side by 6.]

Step: 8

n = 2

[Simplify.]

Step: 9

There are 2 adults and 4 children.

Correct Answer is : 2, 4

Q15A box of 83 fruits containing cherries and oranges costs $440. How many fruits of each kind are there in the box, if two cherries cost $12 and two oranges cost $10?
A. 22, 60
B. 25 , 66
C. 37, 58
D. 25, 58

Solutions

Step: 1

Let n be the number of cherries. Number of oranges is 83 - n.

Step: 2

Unit price of cherries = 122 = $6

[2 cherries cost $12.]

Step: 3

Unit price of oranges = 102 = $5

[2 oranges cost $10.]

Step: 4

6n + 5(83 - n) = 440

[Original equation.]

Step: 5

6n + 5 x 83 - 5n = 440

[Simplify.]

Step: 6

n + 415 = 440

[Subtract.]

Step: 7

n = 25

[Subtract 415 from each side.]

Step: 8

The box contains 25 cherries and 58 oranges.

Correct Answer is : 25, 58

Solved Examples and Worksheet for Applications of Linear Equations

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