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A boy bought 3 cakes and 4 pies from a shop and received $7.50 change from $40. If he had bought 4 cakes and 3 pies from the same shop, then he would have received $0.75 change instead. How much did he pay for each cake and each pie?

Answer :

Answer: the cost of a cake is $8.5

the cost of a pie is $1.75

Step-by-step explanation:

Let x = the cost of a cake

Let y = the cost of a pie

A boy bought 3 cakes and 4 pies from a shop and received $7.50 change from $40. This means that the cost of the 3 cakes and 4 pies is 40-7.5 = $32.5. Therefore,

3x + 4y = 32.5 - - - - - - - -1

If he had bought 4 cakes and 3 pies from the same shop, then he would have received $0.75. This means that the cost of the 4 cakes and 3 pies is 40-0.75 = $39.25. Therefore,

4x + 3y = 39.25 - - - - - - - -2

Multiply equation 1 by 4 and equation 2 by 3. It becomes

12x + 16y = 130

12x + 9y = 117.75

Subtracting ,

7y = 12.25

y = 12.25/7 = 1.75

From equation 1,

3x = 32.5 - 4y

3x = 32.5 - 4×1.75 = 32.5 - 7

3x = 25.5

x = 25.5/3 = $8.5

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