# M7 2 math module 7 solutions to exercises shop at

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M7-2 MATH MODULE 7: SOLUTIONS TO EXERCISES

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shop at Curly’s or Larry’s if and only if the average price of all goods is the same at both stores, in other words if 0.5( P CC + P CE ) = 0.5(1.6 P CC + 0.6 P CE ). The left-hand side is the average cost per item at Curly’s, and the right-hand side is the average cost per item at Larry’s. If the left-hand side is greater than the right- hand side, Curly’s is more expensive. If the right-hand side is greater than the left- hand side, Larry’s is more expensive. Rearranging terms, we find that the two stores are equally expensive if P CC /P CE = 2/3. If P CC /P CE > 2/3, then Larry’s is more expen- sive and if P CC /P CE < 2/3, then Curly’s is more expensive. [You can also express the relationship in terms of Larry’s prices, and show that equal expenditure in both stores requires 0.5([10/6] P LC + [10/16] P LE ) = 0.5( P LC + P LE ). As an exercise, you may want to use this equation to work out the equivalent results as to where you should shop, in terms of P LC /P LE .] M7-3 MATH MODULE 7: SOLUTIONS TO EXERCISES
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