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?
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.