Q58. - Algebra 2

Question

Step-by-Step Solution

Answer

Maximum number of miles a person can drive is 513 miles.

Step 1 -Write an inequality

Let the number of miles a person can drive be x

As rent for 1 mile is $\$0.15$, so rent for x miles is $\$0.15x$

Since, sum of $\$12.95$ and $\$0.15x$ gives total rent of each day which must be less than or equal to $\$90$. Thus, inequality is 

$12.95+0.15x\le 90$

Step 2 - Write properties of inequality

Properties of inequalities are written in following table:

Step 3 - Simplify 12 . 95 + 0 . 15 x ≤ 90

To simplify given inequality, use subtraction and division property of inequalities. Subtract a number from both sides of inequality does not change its sign. Also divide both sides by same positive number does not reverse the sign of inequality as shown below

 $\begin{array}{c}12.95-12.95+0.15x\le 90-12.95\\ 0.15x\le 77.05\\ \frac{0.15x}{0.15}\le \frac{77.05}{0.15}\\ x\le 513.67\end{array}$

Thus, maximum number of miles a person can drive is 513 miles.