Q40. - Algebra 2

Question

Juan’s parents gave him $\backslash (35$ to spend at the State Fair. He spends $\backslash )13.25$ for food. If rides at the fair cost $\$1.50$ each, solve the inequality $1.5n+13.25\le 35$ to determine how many rides he can afford.

Step-by-Step Solution

Answer

Juan can afford at most 14 rides.

Step 1 - Write properties of inequality

Properties of inequalities are written in following table:

Step 2 - Simplify 1.5 n + 13.25 ≤ 35

To simplify given inequality, first use subtraction property of inequalities. Subtract same number from both sides does not change the sign of inequality as shown below

$\begin{array}{c}1.5n+13.25\le 35\\ 1.5n+13.25-13.25\le 35-13.25\\ 1.5n\le 21.75\end{array}$

Step 3 - Simplify 1.5 n ≤ 21.75

To simplify, use division property of inequalities. Divide both sides by same positive number does not reverse the sign of inequality as shown below

 $\begin{array}{c}\frac{1.5n}{1.5}\le \frac{21.75}{1.5}\\ n\le 14.5\end{array}$

As, $n$ represents number of rides which can only be whole number so Juan can afford at most 14 rides.