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Q27.

Expert-verified
Found in: Page 133

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Toll Booth You lose your electronic tag that you use to pay tolls on the highway in your city. It costs you $24 to replace the tag. The cost of one toll when you don’t use the tag is$3. The cost of the same toll when you do use the tag is $1.50. How many times will you have to use the tag to pay for the tolls in order for the total cost to be same as not using the tag? I will have to use the tag 16 times. See the step by step solution ### Step by Step Solution ## Step-1 – Given The cost of replacing a tag =$24

The cost of one toll without the use of tag = $3 The cost of one toll with the use of tag =$1.50

## Step-2 – To determine

We have to find the number of times the tag can be used to pay the tolls.

## Step-3 – Calculation

Let the number of tolls = x.

So,

The cost of x times of toll without the use of tag = 3x

The cost of x times of toll with the use of tag = 1.5x

Hence, the equation is, $24+1.5x=3x$

$\begin{array}{l}24+1.5x=3x\text{write the original equation}\\ \text{24}+1.5x-1.5x=3x-1.5x\text{subtract 1}.5x\text{from both sides}\\ \text{24}=1.5x\text{simplify}\\ \frac{24}{1.5}=\frac{1.5x}{1.5}\text{divide each side by 1.5}\\ \text{x}=16\text{simplify}\end{array}$

So, I will have to use the tag 16 times.