A corner store sells two kinds of baked goods: cakes and pies. A cake costs $5 and a pie costs $7. In one day, the store sold 15 baked goods for a total of $91. How many cakes did they sell?
Let's say the store sold c cakes and p pies.
We know that cakes cost 5*c and pies cost 7*p.
We also know that the store sold 15 baked goods, so c + p = 15.
The total amount of money earned is $91, or 5*c + 7*p = $91.
Let's solve this system of equations. Multiply the first equation by 5 and subtract it from the second equation: 5*c + 7*p - 5*c - 5*p = $91 - $75.
This simplifies to 2*p = $16, so p = $16 / 2 = <<16/2=8>>8.
Since c + p = 15, then c = 15 - 8 = <<15-8=7>>7. Answer: \boxed{7}.
Let's use algebra to solve this problem step-by-step.
Let's assume the number of cakes sold is represented by the variable "C" and the number of pies sold is represented by the variable "P."
From the given information, we can create two equations.
1. The total number of baked goods sold: C + P = 15
2. The total sales from all the baked goods: 5C + 7P = 91
We have a system of equations that we can solve simultaneously.
We can solve for "C" in the first equation by subtracting "P" from both sides: C = 15 - P.
Now, we can substitute this value of "C" into the second equation: 5(15 - P) + 7P = 91.
Expanding the equation, we get: 75 - 5P + 7P = 91.
Combining like terms, we have: 2P = 16.
Dividing both sides of the equation by 2, we get: P = 8.
Now, substitute this value of "P" back into the first equation: C + 8 = 15.
Subtracting 8 from both sides, we get: C = 15 - 8.
Simplifying further, C = 7.
Therefore, the store sold 7 cakes.
To solve this problem, we can set up a system of equations based on the given information. Let's denote the number of cakes sold as "x" and the number of pies sold as "y".
From the given information, we can establish two equations:
1. The total number of baked goods sold: x + y = 15
2. The total revenue from the sales: 5x + 7y = 91
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution for this example.
From equation 1: x = 15 - y
Substituting this into equation 2: 5(15 - y) + 7y = 91
Now, we can simplify and solve for y:
75 - 5y + 7y = 91
2y = 91 - 75
2y = 16
y = 8
By substituting the value of y back into equation 1, we can find the value of x:
x + 8 = 15
x = 15 - 8
x = 7
Therefore, the store sold 7 cakes.
In summary, the store sold 7 cakes and 8 pies to make a total of 15 baked goods.