Question

use the following word problem to answer the questions on the right. kenzie wants to buy some body spray for her friends birthday. she wants to keep the cost between $10.00 and $15.00. bath and body works is having a sale, so she can buy a bottle of body spray for $1.25 each. what is the range of body sprays she can buy for her friend? 2.10 question 6 complete parts a - e below. (a) write the inequality for the word problem on the left. inequality: (b) solve the inequality from part a. round to the nearest hundredths place as needed. solution: (c) graph the solution.

Explanation:

Step1: Define variable

Let $x$ be the number of body - sprays. The cost of $x$ body - sprays is $1.25x$. Since the cost should be between $10$ and $15$, the inequality is $10\leq1.25x\leq15$.

Step2: Solve left - hand side of inequality

Divide both sides of $10\leq1.25x$ by $1.25$. We get $\frac{10}{1.25}\leq x$, so $8\leq x$.

Step3: Solve right - hand side of inequality

Divide both sides of $1.25x\leq15$ by $1.25$. We get $x\leq\frac{15}{1.25}=12$.

Answer:

(a) Inequality: $10\leq1.25x\leq15$
(b) Solution: $8\leq x\leq12$
(c) To graph the solution on a number line: Draw a number line. Mark points $8$ and $12$. Use closed circles at $8$ and $12$ (because the inequality includes equality) and shade the region between them.