Coby sells apples and bananas at his fruit store. He charges $6 for a pound of bananas, and $8 for a pound of apples. If a customer buys a total of 13 pounds of fruit and is charged $92, how many pounds of bananas did he buy? Also, how many pounds of apples did he get?
a+b = 13
8a+6b = 92
now solve for a and b
cant cheat on a test man-
To solve this problem, we'll use a system of equations. Let's assign variables to the unknown quantities:
Let "b" represent the number of pounds of bananas.
Let "a" represent the number of pounds of apples.
According to the problem, the store charges $6 for a pound of bananas and $8 for a pound of apples. We also know that the customer bought a total of 13 pounds of fruit and was charged $92.
We can express these facts with two equations:
1. The total weight equation: b + a = 13
2. The total cost equation: 6b + 8a = 92
Now we can solve the system of equations by substitution or elimination. Let's use elimination:
Multiply the first equation by 6 to make the coefficients of "b" equal in both equations:
6(b + a) = 6(13)
6b + 6a = 78
Now we have the system of equations:
6b + 8a = 92
6b + 6a = 78
Subtract the second equation from the first:
(6b + 8a) - (6b + 6a) = 92 - 78
2a = 14
a = 7
We've found that "a," the number of pounds of apples, is 7.
Now we can substitute this value back into the first equation to find the value of "b" (the number of pounds of bananas):
b + 7 = 13
b = 13 - 7
b = 6
So, the customer bought 6 pounds of bananas and 7 pounds of apples.