On Saturday barkers bake sale sold 8 cakes and 12 pies, making a total of $164. On Sunday they sold 10 cakes and 4 pies, earning $128.

What is the price of cake?
What is the price of pie?

User Icon for bobpursley bobpursley answered
7 years ago

10C+4P=128

8C+12P=164

multipy top equation by 3
30C+12P=384
8C+ 12P=164
subtract eq 2 from 1
22C=220
C=10 dollars pre cake
then solve for P, the pie cost.

User Icon for Explain Bot Explain Bot answered
11 months ago

To find the price of cake and pie, we can set up a system of equations using the given information.

Let's denote the price of a cake as "C" and the price of a pie as "P".

From the information given on Saturday:
8C + 12P = 164

And from the information given on Sunday:
10C + 4P = 128

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method:

Multiplying the first equation by 5 and the second equation by 2 to eliminate the "P" term:
40C + 60P = 820 (Equation A)
20C + 8P = 256 (Equation B)

Subtracting Equation B from Equation A:
(40C + 60P) - (20C + 8P) = 820 - 256
20C + 52P = 564

Divide both sides of this equation by 4 to simplify it further:
5C + 13P = 141 (Equation C)

Now, we have a new equation (Equation C) that relates the price of cakes and pies.

We can solve this equation for one variable in terms of the other. Let's solve Equation C for "P":

P = (141 - 5C) / 13

Now that we have the value of "P" in terms of "C", we can substitute this expression into one of the original equations to find the value of "C".

Substituting P in the first equation:
8C + 12[(141 - 5C) / 13] = 164

Multiplying through by 13 to get rid of the denominator:
104C + 12(141 - 5C) = 2132

Distributing and simplifying this equation:
104C + 1692 - 60C = 2132

Combine like terms:
44C + 1692 = 2132

Subtracting 1692 from both sides:
44C = 440

Dividing both sides by 44:
C = 10

So, the price of a cake is $10.

Now we can substitute this value into one of the original equations to find the price of a pie.

Using the first equation:
8(10) + 12P = 164

Simplifying:
80 + 12P = 164

Subtracting 80 from both sides:
12P = 84

Dividing both sides by 12:
P = 7

Therefore, the price of a pie is $7.