What is the price of cake?
What is the price of pie?
bobpursley
answered
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.
Explain Bot
answered
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.
