﻿ Solving Multi Step Equations Worksheet | Problems & Solutions

# Solving Multi Step Equations Worksheet

Solving Multi Step Equations Worksheet
• Page 1
1.
A man spends half of his salary on household expenses, $\frac{1}{4}$th on rent and $\frac{1}{5}$th on travel expenses. He deposits the rest in a bank. If he deposits $50 monthly in the bank account, then find his monthly salary.  a.$965 b. $1,000 c.$1,725 d. $1,250 #### Solution: Let x be the monthly salary of a man. Given, the amount spent by the man for household expenses = x / 2. The amount spent by the man towards rent = x / 4. The amount spent by the man towards travel expenses = x / 5. The amount deposited in the bank = Total salary - household expenses - amount spent on rent - travel expenses. x - x2 -x4 -x5 = 50 20x - 10x - 5x - 4x20 = 50 x20 = 50 x = 50 × 20 = 1000 Therefore, the monthly salary of the man is$1,000.

2.
Solve:
7$x$ + 4 = 25
 a. 3 b. 5 c. 4 d. 2

#### Solution:

7x + 4 = 25
[Original equation.]

7x + 4 - 4 = 25 - 4
[Subtract 4 from each side.]

7x = 21
[Simplify.]

7x7 = 217
[Divide each side by 7.]

x = 3
[Simplify.]

3.
Solve:
5$x$ - 3 = 12
 a. 5 b. 4 c. 3 d. 2

#### Solution:

5x - 3 = 12
[Original equation.]

5x - 3 + 3 = 12 + 3

5x = 15
[Simplify.]

5x5 = 155
[Divide each side by 5.]

x = 3
[Simplify.]

4.
Solve:
2$a$ + 2 = 4
 a. 1 b. 4 c. 6 d. 3

#### Solution:

2a + 2 = 4
[Original equation.]

2a + 2 - 2 = 4 - 2
[Subtract 2 from each side.]

2a = 2
[Simplify.]

2a2 = 22
[Divide each side by 2.]

a = 1
[Simplify.]

5.
Find the value of $a$, if the perimeter of the regular pentagon is 55 cm.

 a. 7 b. 8 c. 6 d. 5

#### Solution:

The perimeter of a figure is the sum of the lengths of all its sides.

The perimeter of the regular pentagon = 5 × length of one of its sides.
[Since, lengths of all the sides of a regular pentagon are equal.]

5 × (a + 5) = 55
[Substitute the length.]

5(a) + 5(5) = 55
[Use distributive property.]

5a + 25 = 55
[Simplify.]

5a = 30
[Subtract 25 from each side.]

5a5 = 305
[Divide each side by 5.]

a = 6

So, the value of a is 6.

6.
Solve:
8$z$ + 3 = - 21
 a. - 5 b. 4 c. - 3 d. 2

#### Solution:

8z + 3 = - 21
[Original equation.]

8z + 3 - 3 = - 21 - 3
[Subtract 3 from each side.]

8z = - 24
[Simplify.]

8z8 = - 24 / 8
[Divide each side by 8.]

z = - 3
[Simplify.]

7.
Solve:
- $a$ + (21$a$ - 8) = 92
 a. 5 b. 80 c. 7.69 d. 4.2

#### Solution:

- a + (21a - 8) = 92
[Original equation.]

20a - 8 = 92
[Combine like terms.]

20a - 8 + 8 = 92 + 8

20a = 100
[Simplify.]

20a20 = 10020
[Divide each side by 20.]

a = 5
[Simplify.]

8.
A bookseller sold books worth $2,000 in a week. The cost of each book is$20. How many books did he sell during the week, if he earned a profit of \$200?
 a. 102 b. 75 c. 90 d. 115

#### Solution:

Let b be the number of books sold.

Amount for which books were sold for = profit + cost of b books

2000 = 200 + 20b
[Write an algebraic equation.]

2000 - 200 = 200 + 20b - 200
[Subtract 200 from each side.]

1800 = 20b
[Combine like terms.]

180020 = 20b20
[Divide each side by 20.]

90 = b
[Simplify.]

The bookseller sold 90 books in that week.

9.
Solve:
$\frac{m}{120}$ - 4 = - 7
 a. - 360 b. 360 c. - 370 d. - 350

#### Solution:

m120 - 4 = - 7
[Original equation.]

m120 - 4 + 4 = - 7 + 4

m120 = - 3

120 × m120 = 120(- 3)
[Multiply each side by 120.]

m = - 360
[Simplify.]

10.
Solve:
21 = + 17
 a. - 4 b. - 20 c. 5 d. - 1

#### Solution:

21 = k- 5 + 17
[Original equation.]

21 - 17 = k(- 5) + 17 - 17
[Subtract 17 from each side.]

4 = k- 5
[Simplify.]

(- 5)4 = - 5 × k- 5
[Multiply each side by - 5.]

- 20 = k
[Simplify.]

k = - 20