The restaurant manager wants to find how much they are spending for pies and cakes. Last week they payed 204$ for 12 pies and 8 cakes

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The restaurant manager wants to find how much they are spending for pies and cakes. Last week they payed 204$ for 12 pies and 8 cakes. This week, they paid $129 for 5 pies and 7 cakes.

Let's say the cost of pies is x

Let's say the cost of cake is y.

We'll then use the information given to make an equation which will be:

Last week they payed 204$ for 12 pies and 8 cakes. This will be:

12x + 8y = 204 i

This week, they paid $129 or 5 pies and 7 cakes. This will be:

5x + 7y = 129 ii

Therefore,

12x + 8y = 204 i

5x + 7y = 129 ii

Multiply equation i by 5

Multiply equation ii by 12

60x + 40y = 1020 iii

60x + 84y = 1548 iv

Subtract iii from iv.

44y = 528

y = 528/44

y = 12

The cost of cake is $12.

From equation i,

12x + 8y = 204

12x + 8(12) = 204

12x + 96 = 204

12x = 204 - 96

12x = 108

x = 108/12

x = 9

The cost of pies is $9.

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