StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q27.

Expert-verifiedFound in: Page 133

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.

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

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

Let the number of tolls = *x*.

So,

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

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

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.

94% of StudySmarter users get better grades.

Sign up for free