Question
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?
2
4
10
14
2
4
10
14
Answers
GPT-4o mini
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.
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.