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.
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Question

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

UpStudy AI · Accepted Answer

Let's denote the time it takes Luke to do a push-up as $$ p $$ seconds and the time it takes him to do a sit-up as $$ s $$ seconds.

From the given information, we can write the following system of equations:

1. $$ 8p + 15s = 69 $$ (Luke does 8 push-ups and 15 sit-ups in 69 seconds)
2. $$ 15p + 17s = 96 $$ (Luke needs 96 seconds to do 15 push-ups and 17 sit-ups)

We will solve this system of equations using the elimination method to find the values of $$ p $$ and $$ s $$.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}8p+15s=69\15p+17s=96\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}p=\frac{69-15s}{8}\15p+17s=96\end{array}ight.$$
- step2: Substitute the value of $$p:$$
  $$15	imes \frac{69-15s}{8}+17s=96$$
- step3: Simplify:
  $$\frac{15\left(69-15sight)}{8}+17s=96$$
- step4: Multiply both sides of the equation by LCD:
  $$\left(\frac{15\left(69-15sight)}{8}+17sight)	imes 8=96	imes 8$$
- step5: Simplify the equation:
  $$1035-89s=768$$
- step6: Move the constant to the right side:
  $$-89s=768-1035$$
- step7: Subtract the numbers:
  $$-89s=-267$$
- step8: Change the signs:
  $$89s=267$$
- step9: Divide both sides:
  $$\frac{89s}{89}=\frac{267}{89}$$
- step10: Divide the numbers:
  $$s=3$$
- step11: Substitute the value of $$s:$$
  $$p=\frac{69-15	imes 3}{8}$$
- step12: Simplify:
  $$p=3$$
- step13: Calculate:
  $$\left\{ \begin{array}{l}p=3\s=3\end{array}ight.$$
- step14: Check the solution:
  $$\left\{ \begin{array}{l}p=3\s=3\end{array}ight.$$
- step15: Rewrite:
  $$\left(p,sight) = \left(3,3ight)$$
The solution to the system of equations is $$ p = 3 $$ seconds and $$ s = 3 $$ seconds.

Therefore, it takes Luke 3 seconds to do a push-up and 3 seconds to do a sit-up.
The solution to the system of equations is $$ p = 3 $$ seconds and $$ s = 3 $$ seconds. Therefore, it takes Luke 3 seconds to do a push-up and 3 seconds to do a sit-up.

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