An equation is formed when two equal expressions. The number of merchandise that you would have to purchase in a year to pay the same amount under both plans is 800.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that you are choosing between two plans at a discount warehouse.
The cost for x number of merchandise under plan A, which offers an annual membership fee of $120 and you pay 80% of the manufacturer's. Therefore, the cost will be,
Cost = 120 + 0.8x
The cost for x number of merchandise under plan B, which offers an annual membership fee of $40 and you pay 90% of the manufacturer's recommended list price. Therefore, the cost will be,
Cost = 40 + 0.9x
Now, in order to find the number of merchandise that you would have to purchase in a year to pay the same amount under both plans, you need to equate the two equations together. Therefore,
Cost from Plan A = Cost from Plan B
120 + 0.8x = 40 + 0.9x
120 - 40 = 0.9x - 0.8x
80 = 0.1x
x = 80 / 0.1
x = 800
Hence, the number of merchandise that you would have to purchase in a year to pay the same amount under both plans is 800.
Further, the cost for each plan for 800 merchandise can be written as,
PlanA,
Cost = 120 + 0.8(800)
= $760
Plan B,
Cost = 40 + 0.9(800)
= $760
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