Question

shopping the shoppers reward program offers discounts with membership. how much would you need to spend to earn more in discounts than you pay for the membership?
the variable x represents the ▼ select choice ▼.
the situation can be represented by the inequality ▼ select choice ▼ ▼ select choice ▼.
spend ▼ select choice ▼ than ▼ select choice ▼ to earn more in discounts than you pay for the membership.

shoppers reward program
earn discounts and help the community!
enroll for just $25 and
we will donate $10 to
the local community
resources center!
enjoy a 15% discount
on all your purchases
this year!

Explanation:

Step1: Define variables and discount

Let \( x \) be total purchases. Discount is \( 15\% \) of \( x \), so discount \( = 0.15x \). Membership cost is \( \$25 \).

Step2: Set up inequality

We want discount > membership cost: \( 0.15x > 25 \).

Step3: Solve for \( x \)

Divide both sides by \( 0.15 \): \( x > \frac{25}{0.15} \approx 166.67 \).

Answer:

You need to spend more than \(\$166.67\) (or \( x > \frac{500}{3} \)) to earn more in discounts than the \(\$25\) membership cost. The inequality is \( 0.15x > 25 \), and solving gives \( x > \frac{25}{0.15} \approx 166.67 \).