﻿ Verbal and Algebraic Expressions Worksheet | Problems & Solutions

# Verbal and Algebraic Expressions Worksheet

Verbal and Algebraic Expressions Worksheet
• Page 1
1.
Renny bought 20 books each of which costs $7. The total bill is$120 which includes a discount. What is the discount on each book?
 a. $1 b.$3 c. $2 d.$5

#### Solution:

[Verbal model.]

Cost of each book = $7 Number of books = 20 Let the discount on each book =$x

Amount of the bill = $120 (7) (20) - (20) (x) = 120 [Algebraic model.] 20x = 20 [Simplify.] x = 1 [Use Multiplication Facts to solve.] The discount on each book =$1.

2.
The rate of growth of a vine is 1 foot per day. If the vine was 91 feet long on July first, then how long was it on May first?
 a. 40 feet b. 25 feet c. 35 feet d. 30 feet

#### Solution:

[Verbal model.]

Let the length of vine on May1 = x feet
[Initial length.]

Rate of growth of the vine = 1 foot per day

Time = Number of days form May 1 to July 1 = 61days

Length of the vine on july1 = 91 feet
[Final length.]

x + (1) × (61) = 91
[Algebraic model.]

x = 30
[Solve for x.]

So, the length of the vine on May1 = 30 feet.

3.
Robert and his friends went to a magic show with their families. Cost of ticket for each adult was $25 and for each child was$12. The group had 14 adults and the total cost for the tickets was $518. How many children were there in the group?  a. 16 b. 17 c. 15 d. 14 #### Solution: [Verbal model.] Cost of ticket for adult =$25

Number of adults in the group = 14

Cost of ticket for child = $12 Let the number of children in the group = x Total cost =$518

(12) × (x) + (25) × (14) = 518
[Algebraic model.]

12x = 168
[Simplify.]

x = 14
[Use Multiplication Facts to solve.]

The number of children in the group = 14.

4.
Nathan has taken a car on lease under an agreement that requires a down payment of $1,500 and$250 per month for 24 months. He also has to pay $0.25 per mile on each mile driven over 20,000 miles. Choose the correct model for the total amount A, that Nathan has to pay for the car, if he drives more than 20,000 miles. (Assume M represents the number of miles driven over 20,000 miles.)  a. A =$(0.25) (20,000 - M) b. A = $1500 +$(250)(24) + $(0.25) (M) c. A =$(250) (24) + $(0.25) (20,000 - M) d. A =$1500 + $(0.25) (20,000 - M) #### Solution: [Verbal model.] Down payment =$1,500

Monthly installment = $250 Number of months = 24 Additional charge per mile for all the number of miles, M, driven over 20,000 miles =$0.25M

Total amount = A

A = $1500 +$(250) (24) + $(0.25) (M) [Substitute.] The model which gives the total amount that Nathan has to pay for the car is A =$1500 + $(250) (24) +$(0.25) (M).

5.
To raise $4,000 for a charity, a club is selling magazine subscriptions at$10 each. How many subscriptions does the club need to sell to raise the amount?
 a. 450 b. 500 c. 400 d. 350

#### Solution:

[Verbal model.]

Cost of each subscription = $10 Let the number of subscriptions = n Amount to be raised =$4,000

10 × n = 4000
[Algebraic model.]

n = 400
[Use Multiplication Facts to solve.]

The number of subscriptions the club need to sell is 400.