﻿ Algebra Word Problems - Page 5 | Problems & Solutions

# Algebra Word Problems - Page 5

Algebra Word Problems
• Page 5
41.
A number consists of two digits whose sum is 7. When 9 is added to the number, the digits are reversed. What is the number?
 a. 34 b. 43 c. 52 d. 61

42.
Find the number which begins the sequence.

 a. 45 b. 35 c. 50 d. 25

43.
When a number is multiplied by 4 and then added to 6, the result is 26. What is this number?
 a. 6 b. 9 c. 5 d. 7

44.
A mother wants to distribute candies to her two sons according to the ratio of their ages. The younger son is 7 years old and the older one is 11 years old. If the younger son receives 21 candies, then how many candies will the elder son receive?
 a. 33 b. 34 c. 31 d. 32

45.
Victor has read 72 pages of a 264-page book. He reads 24 pages each day. How many days will he take to finish the book?
 a. 10 b. 7 c. 8 d. 9

#### Solution:

Let p be the number of days required to finish reading the book.

72 + 24 × p = 264
[Write an equation.]

72 - 72 + 24p = 264 - 72
[Subtract 72 from both sides.]

24p = 192
[Combine like terms.]

p = 192 / 24
[Divide both sides by 24.]

p = 8
[Simplify.]

So, Victor takes 8 days to finish reading the whole book.

46.
Two packets of meat together weigh 4.65 kg. If one packet weighs 3.56 kg, then how much does the other packet weigh?
 a. 1.44 kg b. 4.30 kg c. 0.74 kg d. 1.09 kg

#### Solution:

The weight of other packet = Total weight of two packets - Weight of one packet

The weight of the other packet = 4.65 - 3.56
[Substitute the values.]

The weight of the other packet = 1.09 kg
[Subtract.]

47.
The total toll for 1 car and 3 bicycles to cross a bridge is $3.80. The toll for one car is$1.40 more than that for a bicycle. Find the toll for a bicycle to cross the bridge.
 a. $0.40 b.$0.80 c. $0.60 d.$2.00

#### Solution:

Let x be the toll charge for a bicycle to cross the bridge.

The toll charge for a car = x + 1.40

Toll charge for 1 car + 3 × Toll charge for 1 bicycle = $3.80 The toll charge for 1 car and 3 bicycles = (x + 1.40) + 3x = 3.80 [Substitute the values.] 4x + 1.40 = 3.80 [Combine like terms.] 4x + 1.40 - 1.40 = 3.80 - 1.40 [Subtract 1.40 from both sides.] 4x = 2.40 [Simplify.] x = 2.40 / 4 = 0.60 [Divide.] The toll charge of a bicycle to cross the bridge is$0.60.

48.
A baby girl weighed 3.4 kg at birth. She gained 0.15 kg per week. How old was she when she weighed 5.2 kg?
 a. 12 weeks b. 13 weeks c. 17 weeks d. 11 weeks

#### Solution:

Let a be the age of the baby when she weighs 5.75 kg.

3.4 + a × 0.15 = 5.2
[Original equation.]

3.4 - 3.4 + a × 0.15 = 5.2 - 3.4
[Subtract 3.4 from both sides.]

a × 0.15 = 1.8
[Simplify.]

a = 1.8 / 0.15
[Divide both sides by 0.15.]

a = 12
[Simplify.]

The baby was 12 weeks old when she weighed 5.2 kg.

49.
A pencil and an eraser together cost $1.40. The pencil costs$1 more than the eraser. How much does the pencil cost?
 a. $1 b.$1.40 c. $1.20 d. None of the above #### Solution: Let the cost of the eraser be$a.

The cost of pencil = $(a + 1) Cost of pencil + Cost of eraser =$1.40

(a + 1) + a = 1.40
[Write an equation.]

2a + 1 = 1.40

2a = 1.40 - 1
[Subtract 1 from both sides.]

2a = 0.40
[Subtract.]

a = 0.20
[Divide both sides by 2.]

The cost of a pencil = 1 + 0.20 = \$1.20

50.
$\frac{4}{5}$ of the students from Ursula's class went on a picnic. How many students did not go to the picnic?
 a. $n$ b. $\frac{n}{6}$ c. $\frac{n}{4}$ d. $\frac{n}{5}$

#### Solution:

Let n be the number of students in the class.

The part of the class who went on a picnic = 4 / 5 × n = (4n / 5)
[Multiply.]

The number of students who stayed in the school = n - 4n / 5

= n / 1 - 4n / 5
[Write n as n / 1.]

= 5n / 5 - 4n / 5
[Multiply and divide the numerator and denominator of the first fraction by 5.]

= n / 5