14 c + 8 p = 144
c + p = 12 so p = (12-c)
14 c + 8 (12-c) = 144
solve for c
c + p = 12 so p = (12-c)
14 c + 8 (12-c) = 144
solve for c
Let's assume the number of cakes sold is represented by 'c' and the number of pies sold is represented by 'p'.
According to the problem, we know that a cake costs $14 and a pie costs $8. So we can set up two equations based on the number of cakes and pies sold:
c + p = 12 (since the store sold a total of 12 baked goods)
14c + 8p = 144 (since the total sales amounted to $144)
Now, we have a system of two equations with two variables. We can solve this system to find the values of 'c' and 'p'.
Let's solve the first equation for 'p':
p = 12 - c
Now substitute this value of 'p' in the second equation:
14c + 8(12 - c) = 144
Simplify the equation:
14c + 96 - 8c = 144
6c + 96 = 144
Subtract 96 from both sides:
6c = 48
Divide both sides by 6:
c = 8
So, the store sold 8 cakes.
Therefore, the number of pies sold can be represented by the expression (12 - x).
The cost of each cake is $14, so the total revenue from cake sales can be calculated as 14x.
Similarly, the cost of each pie is $8, so the total revenue from pie sales can be calculated as 8(12 - x).
Given that the total revenue from all the baked goods sold is $144, we can set up the equation:
14x + 8(12 - x) = 144
Now let's solve this equation step by step:
14x + 96 - 8x = 144
Combine like terms:
6x + 96 = 144
Subtract 96 from both sides of the equation to isolate the variable term:
6x = 48
Now, divide both sides of the equation by 6:
x = 8
Therefore, the store sold 8 cakes.