# Algebra Word Problems - Page 7

Algebra Word Problems
• Page 7
61.
Justin spends $\frac{3}{4}$of his income on food. Find the amount he is left with.
 a. $\frac{1}{3}$ of his income b. $\frac{1}{2}$ of his income c. $\frac{1}{4}$ of his income d. $\frac{1}{8}$ of his income

#### Solution:

Let 'n' be Justin's income.

The part of the income spent on food commodities = 3 / 4x n = ( 3n / 4 )

The amount left with Justin = n - 3n / 4

= n1- 3n4
[Write n as n / 1 .]

= 4n4- 3n4
[Multiply and divide the numerator and denominator of the first fraction by 4.]

= n4

The amount left with Justin is 1 / 4of his income.

62.
Josh earns $22 per hour. How many hours does he work, if he is paid$198?
 a. 8 hours b. 9 hours c. 7 hours d. 10 hours

#### Solution:

Let P be the total number of hours taken to earn $198. Amount earned by Josh per hour =$22

= $22P Amount earned by Josh in P hours =$22 × P
[Multiply.]

22 P = 198
[Substitute the values.]

P = 19822
[Divide each side by 22.]

P = 9
[Divide.]

So, the number of hours taken to earn \$198 is 9 hours.

63.
Frank is 16 times older than his son John. If his son is 2 years old, find Frank's age.
 a. 35 years b. 29 years c. 32 years d. 27 years

#### Solution:

Let x be the age of Frank.

x = 16 x 2

x = 32
[Multiply.]

So, Frank is 32 years old.

64.
One of the angles of a triangle is 90o. Find the remaining two angles if their difference is 20o.
 a. 35o, 55o b. 70o, 20o c. 20o, 90o d. 90o, 35o

#### Solution:

Let a represent one angle, the other angle will be a + 20o.
[As per the question.]

90o + a + a + 20o = 180o
[Sum of the angles of a triangle = 180o.]

2a + 110o = 180o
[Solve.]

2a = 70o

a = 35o

a + 20o = 55o

So, the remaining two angles of the triangle are 35o and 55o.

65.
A pop singer gives 54 performances in 81 days. How many days will he take to give 6 performances?
 a. 9 days b. 15 days c. 6 days d. 48 days

#### Solution:

Let x represent the number of days to give 6 performances
[As per the question.]

54 / 81 = 6x
[Equate the number of performances per day.]

54x = 486

x = 9

So, the pop singer will take 9 days to give 6 performances.