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Solving Multi Step Equations Worksheet

Solving Multi Step Equations Worksheet
  • Page 1
 1.  
A man spends half of his salary on household expenses, 1 4th on rent and 1 5th 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.


Correct answer : (2)
 2.  
Solve:
7x + 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.]


Correct answer : (1)
 3.  
Solve:
5x - 3 = 12
a.
5
b.
4
c.
3
d.
2


Solution:

5x - 3 = 12
[Original equation.]

5x - 3 + 3 = 12 + 3
[Add 3 to each side.]

5x = 15
[Simplify.]

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

x = 3
[Simplify.]


Correct answer : (3)
 4.  
Solve:
2a + 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.]


Correct answer : (1)
 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.


Correct answer : (3)
 6.  
Solve:
8z + 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.]


Correct answer : (3)
 7.  
Solve:
- a + (21a - 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
[Add 8 to both sides.]

20a = 100
[Simplify.]

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

a = 5
[Simplify.]


Correct answer : (1)
 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.


Correct answer : (3)
 9.  
Solve:
m120 - 4 = - 7
a.
- 360
b.
360
c.
- 370
d.
- 350


Solution:

m120 - 4 = - 7
[Original equation.]

m120 - 4 + 4 = - 7 + 4
[Add 4 on each side.]

m120 = - 3
[Add.]

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

m = - 360
[Simplify.]


Correct answer : (1)
 10.  
Solve:
21 = k- 5 + 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


Correct answer : (2)

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