Plan A offers an annual membership fee of $72 and you pay 75% of the listed price. Plan B offers an annual membership of $30 and you pay 90% of the listed price. How many dollars of merchandise do you need to purchase so that you pay the same amount under both plans?

Answer: You need to purchase $280 dollars of merchandise to pay the same amount under both plans.

Step-by-step explanation:

Hi, to answer this question we have to write equations for each plan's cost.

The cost of plan a (A) is equal to the annual fee (72) plus y 75% (75/100 = 0.75) of the listed price (x)

A = 72 + 0.75 x

Same process for the cost of plan B (B)

B = 30 + 0.90 x

If both costs are equal

A=B

So:

72 + 0.75 x = 30 + 0.90 x

Solving for x:

72-30 = 0.9x-0.75x

42 = 0.15x

42/0.15 = x

x = $280

You need to purchase $280 dollars of merchandise to pay the same amount under both plans