Question

You are choosing between two plans at a discount warehouse. Plan A offers an annual membership fee of $120 and you pay 80% of the manufacturer's recommended list price. Plan B offers an annual membership fee of $40 and you pay 90% 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 $A be the cost of $q of merchandise under plan A and similarly $B under plan B.
A=120+0.80q, B=40+0.90q
When A=B, 120+0.80q=40+0.90q, 80=0.10q, q=80/0.10=$800.
So you would need to buy $800 of merchandise.
A=B=120+640=40+720=$760 for each plan.