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Algebra Word Problems - Page 7

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


Correct answer : (3)
 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.


Correct answer : (2)
 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.


Correct answer : (3)
 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.


Correct answer : (1)
 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.


Correct answer : (1)

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