For every 8 chin-ups Doug did during the physical fitness test, Adam did 3. Doug was able to do 15 more chin-ups than Adam. How may chin-ups did Adam do?
number of push-ups for Doug = 8x
number of push-ups for Adam = 3x
solve:
8x - 3x = 15
take over
8x - 3x = 15
//Combine like terms
5x = 15
//Divide both sides by 5 to get x on one side
5x / 5 = 15 / 5
x = 3
//Test
8(3) - 3(3) = 15
24 - 9 = 15
To find out how many chin-ups Adam did, we can use the information given about Doug's performance. Let's call the number of chin-ups Doug did "D" and the number of chin-ups Adam did "A".
According to the information, for every 8 chin-ups Doug did, Adam did 3. So we can set up the equation:
D/8 = A/3
We also know that Doug did 15 more chin-ups than Adam, so we can set up another equation:
D = A + 15
Now we have a system of two equations:
D/8 = A/3
D = A + 15
To solve this system, we can use substitution. Rearrange the second equation to solve for D:
D = A + 15
Substitute this expression for D in the first equation:
(A + 15)/8 = A/3
To get rid of the fractions, multiply both sides of the equation by 24 (the least common multiple of 8 and 3):
3(A + 15) = 8A
Distribute the 3 on the left side:
3A + 45 = 8A
Subtract 3A from both sides:
45 = 5A
Divide both sides by 5:
9 = A
Therefore, Adam did 9 chin-ups during the physical fitness test.