Malia did push-ups and pull-ups in her physical education class. She did 24 push-ups and pull-ups combined, with each push-up taking her 2 seconds and each pull-up taking her 4 seconds. If she spent a total of 68 seconds doing the push-ups and pull-ups, how many pull-ups did she do?

Question

2
4
10
14

Answer 1

Let \( p \) be the number of push-ups and \( r \) be the number of pull-ups.

From the problem, we have two equations:

1. The total number of push-ups and pull-ups: \[ p + r = 24 \]

2. The total time spent doing push-ups and pull-ups: \[ 2p + 4r = 68 \]

Now we can simplify the second equation. Dividing everything by 2, we get: \[ p + 2r = 34 \]

Now we have a system of equations:

1. \( p + r = 24 \)
2. \( p + 2r = 34 \)

Next, we can eliminate \( p \) by subtracting the first equation from the second: \[ (p + 2r) - (p + r) = 34 - 24 \] This simplifies to: \[ r = 10 \]

Now that we have the number of pull-ups, we can find the number of push-ups by substituting \( r \) back into the first equation: \[ p + 10 = 24 \] \[ p = 14 \]

Thus, Malia did \( \boxed{10} \) pull-ups.