Question

Toll Booth You lose your electronic tag that you use to pay tolls on the highway in your city. It costs you $24toreplacethetag.Thecostofonetollwhenyoudo{n}^{\prime }tusethetagis$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?

Short answer

I will have to use the tag 16 times.

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, $24+1.5x=3x$

$\begin{array}{l}24+1.5x=3x\text{writetheoriginalequation}\\ \text{24}+1.5x-1.5x=3x-1.5x\text{subtract1}.5x\text{frombothsides}\\ \text{24}=1.5x\text{simplify}\\ \frac{24}{1.5}=\frac{1.5x}{1.5}\text{divideeachsideby1.5}\\ \text{x}=16\text{simplify}\end{array}$

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