A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 40 pounds and each large box of paper weighs 75 pounds. There were 3 times as many small boxes shipped as large boxes shipped and the total weight of all boxes was 975 pounds. Determine the number of small boxes shipped and the number of large boxes shipped.
Rephrase this word problem but with Rocky Balboa and Drago in boxing punching each other.
Rocky Balboa and Drago are facing off in a boxing match. Rocky's punches pack a weight of 40 pounds each, while Drago's punches weigh 75 pounds each. Rocky throws 3 times as many punches as Drago, and the total weight of their punches combined is 975 pounds. Find out how many punches Rocky throws and how many punches Drago throws.
Define the variables and solve them
Let:
- Let x be the number of small boxes shipped (Rocky's punches)
- Let y be the number of large boxes shipped (Drago's punches)
According to the information given:
1. Each small box weighs 40 pounds, so the total weight of small box punches would be 40x.
2. Each large box weighs 75 pounds, so the total weight of large box punches would be 75y.
3. The total weight of all punches is 975 pounds, so we get the equation:
40x + 75y = 975
Also, given that there were 3 times as many small boxes shipped as large boxes, we have the equation:
x = 3y
Substitute x = 3y into the first equation:
40(3y) + 75y = 975
120y + 75y = 975
195y = 975
y = 5
Now, substitute y = 5 back into the second equation to solve for x:
x = 3(5)
x = 15
Therefore, Rocky (small boxes) shipped 15 punches and Drago (large boxes) shipped 5 punches.