Pregunta
Write a system of equations to describe the situation below, solve using elimination, and fill in
the blanks.
When Luke does 8 push-ups and 15 sit-ups, it takes a total of 69 seconds. In comparison, he
needs 96 seconds to do 15 push-ups and 17 sit-ups. How long does it take Luke to do each
kind of exercise?
It takes Luke
seconds to do a push-up and
seconds to do a sit-up.
Submit
the blanks.
When Luke does 8 push-ups and 15 sit-ups, it takes a total of 69 seconds. In comparison, he
needs 96 seconds to do 15 push-ups and 17 sit-ups. How long does it take Luke to do each
kind of exercise?
It takes Luke
Submit
Ask by Pearson Mathis. in the United States
Dec 16,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The solution to the system of equations is
seconds and
seconds. Therefore, it takes Luke 3 seconds to do a push-up and 3 seconds to do a sit-up.
Solución

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Como
Mind Expander
To create the system of equations, let’s denote
as the time (in seconds) it takes Luke to do a push-up and
as the time (in seconds) it takes him to do a sit-up. The problem provides the following information:
-
For 8 push-ups and 15 sit-ups:
-
For 15 push-ups and 17 sit-ups:
Now, to solve this system using elimination, we can first align the coefficients for
or
. Let’s eliminate
by multiplying the first equation by 15 and the second by 8:
-
gives: -
gives:
Now we can subtract the second equation from the first:
This simplifies to:
Dividing both sides by 89:
Now that we have
, we can substitute it back into one of the original equations to find
. Using the first equation:
This simplifies to:
So, it takes Luke
seconds to do a push-up and
seconds to do a sit-up.
It takes Luke
seconds to do a push-up and
seconds to do a sit-up.
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