Final answer:
Coach Ross originally baked 54 brownies. Using the given information that 5/8 were given to the football team, half of the remainder to the cheerleaders, and with 10 left, we worked backwards to determine the total amount baked.
Step-by-step explanation:
Coach Ross baked some brownies and he gave 5/8 of them to the football team. Then, he gave 1/2 of the remaining brownies to the cheerleaders and was left with 10 brownies. To find out how many brownies Coach Ross originally baked, we need to work backwards from the brownies he had left.
Let's denote the total number of brownies baked as x. After giving away 5/8 of the brownies, he had 3/8 of x left. Half of the remaining brownies were given to the cheerleaders, which means he gave away 1/2 of 3/8 of x, leaving him with 1/2 of 3/8 of x. Since we know that he had 10 brownies left, we can set up the equation:
1/2 × (3/8 × x) = 10
Solving for x, we multiply both sides by 2 to get 3/8 x = 20. Then, we multiply both sides by 8/3 to find x.
3/8 x × 8/3 = 20 × 8/3
x = 20 × 8/3
x = 160/3
x = 53.33
We can't have a fraction of a brownie, so we round up to the next whole number, which is 54. Therefore, Coach Ross originally baked 54 brownies.