Question

(HELP ASAP PLEASE!!)

Answer 1

Hello!

The answer is:

It takes Ella 3 seconds to do a push-up and 3 seconds to do a sit up.

Why?

To find how many seconds Ella took to do a push-up and a sit-up we must write two equations using the given information.

Let be "x" the time needed to push-ups and "y" be the time needed to do sit-ups.

So, writing the equations we have:

First equation,

If she can do 13 push-ups and 7 sit-ups in 60 seconds, we have:

$13x+7y=60$

Second equation,

If she can do 13 push-ups and 19 sit-ups in 96 seconds, we have:

$13x+19y=96$

Now, creating a system of equations, and using the reduction method to solve it, we have:

$\left \{ {{13x+7y=60} \atop {13x+19y=96}} \right.$

Multiplying the first equation by -1, we have:

$\left \{ {{-13x-7y=-60} \atop {13x+19y=96}} \right.$

$\left \{ {{-13x-7y=-60} \atop {13x+19y=96}} \right\\\\12y=36\\\\y=\frac{36}{12}=3$

Then, substituting "y" into the first equation, we have:

$13x+7y=60$

$13x+7(3)=60$

$13x+21=60$

$13x=60-21=39$

$x=\frac{39}{13}=3$

Hence, we have that It takes Ella 3 seconds to do a push-up and 3 seconds to do a sit up.

Have a nice day!