#### Solved Examples and Worksheet for Applications of Linear Equations

Q1A number divided by negative 3 is equal to 7. What is the number?
A. - 19
B. - 23
C. 21
D. - 21

Step: 1
Let n be the unknown number.
[Identify the variable.]
Step: 2
n- 3 = 7
[Write the phrase as an equation.]
Step: 3
n- 3 × - 3 = 7 × - 3
[Multiply each side by - 3.]
Step: 4
n = - 21
[Simplify.]
Step: 5
The unknown number is - 21.
Correct Answer is :   - 21
Q2The difference between a number and 37 is 48. What is the number?

A. 4837
B. 5037
C. 4737
D. 4937

Step: 1
Let k be the unknown number.
Step: 2
k - 37 = 48
[Write the equation.]
Step: 3
k - 37 + 37 = 48 + 37
Step: 4
k = 3397
[Simplify.]
Step: 5
k = 4837
[Convert improper fraction into mixed number.]
Step: 6
The number is 4837.
Q3What is the number, if one seventh of the number is 48?
A. 6
B. 7
C. 336
D. 337

Step: 1
Let p be the number.
Step: 2
p × 17 = 48
[Original equation.]
Step: 3
p7 × 7 = 48 × 7
[Multiply each side by 7.]
Step: 4
p = 336
[Simplify.]
Step: 5
The number is 336.
Q4A number divided by 3 equals 15. What is the number?
A. 15
B. 45
C. 18
D. None of the above

Step: 1
Let n be the number.
Step: 2
n3 = 15
[Original equation.]
Step: 3
n3 × 3 = 15 × 3
[Multiply each side with 3.]
Step: 4
n = 45
[Simplify.]
Step: 5
The number is 45.
Q5The sum of 31 and another number is 39. What is the number?
A. 7
B. 10
C. 8
D. 9

Step: 1
Let a be the another number.
Step: 2
31 + a = 39
[Original equation.]
Step: 3
31 + a - 31 = 39 - 31
[Subtract 31 from each side.]
Step: 4
a = 8
[Simplify.]
Step: 5
The other number is 8.
Q6If the sum of 25 and a number is equal to 12, then what is the number?

A. 111
B. 110
C. 1
D. 15

Step: 1
Let n be the number.
Step: 2
25 + n = 12
[Write an eqaution.]
Step: 3
n + 25 - 25 = 12 - 25
[Subtract 25 from both sides.]
Step: 4
= 5 - 410

Step: 5
n = 110
[Simplify.]
Step: 6
So, the number is 110 .
Q7If a number is subtracted from 73, the result is 115. Find the number.

A. 316
B. 215
C. 15
D. 415

Step: 1
Let x be the number.
Step: 2
73 - x = 115
[Write an equation.]
Step: 3
73 - x - 73 = 115 - 73
[Subtract 73 from each side.]
Step: 4
- x = 33-3515
[LCD of 5, 3 is 15.]
Step: 5
- x = - 215
[Subtract 35 from 33.]
Step: 6
x = 215
[Multiply each side by -1.]
Step: 7
The number is 215.
Q8The difference between a number and 37 is 30. What is the number?
A. 70
B. 3037
C. 2947
D. 907

Step: 1
Let k be the unknown number.
Step: 2
k - 37 = 30
[Write the equation.]
Step: 3
k - 37 + 37 = 30 + 37
Step: 4
k = 2137
[Simplify.]
Step: 5
k = 3037
[Convert improper fraction into mixed number.]
Step: 6
The number is 3037.
Q9If the sum of 37 and a number is equal to 23, then what is the number?

A. 521
B. 5
C. 27
D. 522

Step: 1
Let n be the number.
Step: 2
37 + n = 23
[Write an eqaution.]
Step: 3
n + 37- 37 = 23- 37
[Subtract 37 from both sides.]
Step: 4
= 14-921

Step: 5
n = 521
[Simplify.]
Step: 6
So, the number is 521 .
Q10The sum of 25 and another number is 32. What is the number?
A. 32
B. 7
C. 6
D. 57

Step: 1
Let a be the another number.
Step: 2
25 + a = 32
[Original equation.]
Step: 3
25 + a - 25 = 32 - 25
[Subtract 25 from each side.]
Step: 4
a = 7
[Simplify.]
Step: 5
The other number is 7.