math questions

Question

You are choosing between two plans at a discount warehouse.  Plan A offers an annual membership fee of $300 and you pay  70%of the manufacture's recommended list price.  Plan B offers an annual  membership  fee of $40 and you pay 90% of the manufacture'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 of each plan

Answer 1

We can write a system of equations to model this problem. Let x = dollars of merchandise you purchase and let y = how much you actually pay per year. Then:

Plan A: y = 0.7x + 300
Plan B: y = 0.9x + 40

 

Substitute y = 0.7x + 300 into the second equation and solve for x:

 

0.7x + 300 = 0.9x + 40

300 = 0.2x + 40

260 = 0.2x

1300 = x

 

So, you would have to purchase x = $1,300 worth of merchandise to pay the same amount.

 

To find y, plug x = 1300 into the first equation and solve:

 

y = 0.7(1300) + 300

y = 910 + 300

y = 1210

 

So, each plan would cost y = $1,210.

 

 

Check your answer by plugging those values for x and y into the second equation:

 

1210 = 0.9(1300) + 40

1210 = 1170 + 40

1210 = 1210