For every 5 push-ups that Oscar does, Noah does 7 each morning. After Noah drinks a protein shake in the evening, Noah does 9 push-ups for every 3 push-ups Oscar does. If Noah does 99 push-ups after his protein shake, how many push-up will he do in the morning before drinking his protein shake?
To solve this problem, we need to figure out the relationship between the number of push-ups Oscar and Noah do in the morning.
First, let's determine the ratio of push-ups Oscar does to the push-ups Noah does in the morning. We know that for every 5 push-ups Oscar does, Noah does 7 push-ups. So the ratio of Oscar's push-ups to Noah's push-ups is 5:7.
Next, we need to find out how many push-ups Noah does after drinking his protein shake. We are given that for every 3 push-ups Oscar does, Noah does 9 push-ups. So the ratio of Oscar's push-ups to Noah's push-ups after the protein shake is 3:9.
Since we know that Noah does 99 push-ups after his protein shake, we can set up the following equation using the ratios:
(3/9) * 99 = (5/7) * x
Simplifying the equation, we get:
(1/3) * 99 = (5/7) * x
33 = (5/7) * x
To solve for x, we can multiply both sides of the equation by (7/5):
x = (33 * 7) / 5
x = 231 / 5
x = 46.2
Therefore, Noah does approximately 46 push-ups in the morning before drinking his protein shake.