Question

(HELP ASAP PLEASE!!)

When Ella does 13 push-ups and 7 sit-ups, it takes a total of 60 seconds. In comparison, she needs 96 seconds to do 13 push-ups and 19 sit-ups. How long does it take Ella to do each kind of exercise?


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

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=(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=(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!