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QuestionFind the dollar amount of merchandise needed for equal costs under Plan A ($110+0.8x\$ 110 + 0.8x) and Plan B ($20+0.9x\$ 20 + 0.9x).

Studdy Solution

STEP 1

Assumptions1. Plan A has an annual membership fee of 110andyoupay80.PlanBhasanannualmembershipfeeof110 and you pay80% of the manufacturer's recommended list price. . Plan B has an annual membership fee of 20 and you pay90% of the manufacturer's recommended list price.
3. We need to find the amount of merchandise purchase in a year for which the total cost under both plans would be the same.

STEP 2

Let's denote the amount of merchandise you have to purchase in a year as xx.
The total cost under Plan A is the sum of the annual membership fee and the cost of the merchandise, which is80% of xx.
CostA=FeeA+80%×xCost_{A} = Fee_{A} +80\% \times x

STEP 3

Similarly, the total cost under Plan B is the sum of the annual membership fee and the cost of the merchandise, which is90% of xx.
CostB=FeeB+90%×xCost_{B} = Fee_{B} +90\% \times x

STEP 4

We are looking for the amount of merchandise xx for which the total cost under both plans would be the same. So, we set the two costs equal to each other and solve for xx.
CostA=CostBCost_{A} = Cost_{B}

STEP 5

Substitute the values for the costs from steps2 and3 into the equation from step4.
FeeA+80%×x=FeeB+90%×xFee_{A} +80\% \times x = Fee_{B} +90\% \times x

STEP 6

Substitute the values for the fees from the problem into the equation from step5.
$110+80%×x=$20+90%×x\$110 +80\% \times x = \$20 +90\% \times x

STEP 7

To solve for xx, first move the terms involving xx to one side of the equation and the constants to the other side.
80%×x−90%×x=$20−$11080\% \times x -90\% \times x = \$20 - \$110

STEP 8

implify the equation from step7.
10%×x=−$9010\% \times x = -\$90

STEP 9

To solve for xx, divide both sides of the equation by%.
x=−$90/%x = -\$90 /\%

STEP 10

Convert the percentage to a decimal value.
10%=0.10\% =0.x=−$90/0.x = -\$90 /0.

STEP 11

Calculate the value of xx.
x=−$90/0.=−$900x = -\$90 /0. = -\$900The negative sign indicates that you would have to purchase $900 worth of merchandise in a year to pay the same amount under both plans.
The cost for each plan would beFor Plan A 110+80%×$900=$830110 +80\% \times \$900 = \$830 For Plan B 20+90%×$900=$83020 +90\% \times \$900 = \$830

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