The answer is:
It takes Ella 3 seconds to do a push-up and 3 seconds to do a sit up.
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:
[tex]13x+7y=60[/tex]
Second equation,
If she can do 13 push-ups and 19 sit-ups in 96 seconds, we have:
[tex]13x+19y=96[/tex]
Now, creating a system of equations, and using the reduction method to solve it, we have:
[tex]\left \{ {{13x+7y=60} \atop {13x+19y=96}} \right.[/tex]
Multiplying the first equation by -1, we have:
[tex]\left \{ {{-13x-7y=-60} \atop {13x+19y=96}} \right.[/tex]
[tex]\left \{ {{-13x-7y=-60} \atop {13x+19y=96}} \right\\\\12y=36\\\\y=\frac{36}{12}=3[/tex]
Then, substituting "y" into the first equation, we have:
[tex]13x+7y=60[/tex]
[tex]13x+7(3)=60[/tex]
[tex]13x+21=60[/tex]
[tex]13x=60-21=39[/tex]
[tex]x=\frac{39}{13}=3[/tex]
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!
