You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $150 and you pay 30% of the​ manufacturer's recommended list price. Plan B offers an annual membership fee of $80 and you pay 80% of the​ manufacturer's recommended list price. How many dollars of merchandise would you have to purchase in a year to pay the same amount under both​ plans? What will be the cost for each​ plan?

Answer 1

Let the amount of merchandise purchased be x.
For Plan A, the cost would be:
Membership fee + (30% of manufacturer's list price) = 150 + 0.3x

For Plan B, the cost would be:
Membership fee + (80% of manufacturer's list price) = 80 + 0.8x

We want these two costs to be equal, so:
150 + 0.3x = 80 + 0.8x

Simplifying this equation, we get:
0.5x = 70

x = 140

So you would have to purchase $140 worth of merchandise in a year to pay the same amount under both plans.

For Plan A, the cost would be:
150 + 0.3($140) = $192

For Plan B, the cost would be:
80 + 0.8($140) = $192

Therefore, both plans would cost the same amount if you purchase $140 worth of merchandise in a year and the cost would be $192 for each plan.