Question

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 1

$280

Explanation:

According to the question, 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?

We need to answer write the equations for each plan's cost so as to be able to answer the question.

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

A =72 + 0.75(a)

We do same for the cost of plan B (B)

B= 30+ 0.90(a)

Since both costs are to be equal,we have

A=B

Therefore,

72 + 0.75a = 30+ 0.90a

Now let's find the value of a and get the answer to this question

Collecting Like terms,and we have

72-30 = 0.9a - 0.75a

42 = 0.15a

a = 42 ÷ 0.15

a = $280

Therefore,one needs to purchase $280 dollars of merchandise in other to have the same amount under both plans

Answer 2

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

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