a local bake shop sells cookies and cakes. On Monday, Sean bought 3 cookies and 5 cakes and spent $78.75. On Tuesday, Sean bought 8 cookies and 2 cakes and spent $40. find the price of one cookie and one cake.

The price of one cookie is $1.25 and the price of one cake is $15.

Step-by-step explanation:

Trust me I've done this exact equation in my work book i got it correct

Answer: Each cookie cost $1.25 and each cake $15

Step-by-step explanation:

Let's call Co to the price of a cookie, and Ca to the price of a cake; we have that:

3*Co + 5*Ca = $78.75

8*Co + 2*Ca = $40

Now we have a system of equations and we want to solve it, the first step is isolating one of the variables in one of the equations, let's isolate Ca in the second equation:

2*Ca = $40 - 8*Co

Ca = ($40 - 8*Co) / 2 = $20 - 4*Co

Now we can replace it in the first equation, and get:

3*Co + 5 * ($20 - 4*Co) = $78.75

3*Co + $100 - 20*Co = $78.75

-17*Co = $78.75 - $100 = - $21.25

Co = $21.25/17 = $1.25

now we can replace this value in one of the equations and get the price for a cake.

8*$1.25 + 2*Ca = $40

Ca = $20 - 4*$1.25 = $20 - $5 = $15

Each cookie cost $1.25 and each cake $15