Question

Can someone please explain how to do this in detail! (Number 1)

Answer 1

Start by calling the number of home runs Peter hit 'P' and the number Alice hit "A'.

We know that "Altogether, they 18 home runs" so
`A+P=18`.

We laso know that "Peter hit twice the difference of the the number of home runs Alice hit and 6. So:
`P=2(A-6)`

Now we can substitute the second equation into the first:

`A+P=18`

`A+(2(A-6))=18`

And solve for A:

`A+2A-12=18`

`3A=30`

`A=10`

Alice hit 10 home runs.

Now we can plug this known value into the first equation and solve for P:

`A+P=18`

`10+P=18`

`P=8`

Peter hit 8 home runs.

To check, we can use the other equation that we didn't backsubstitute into:


`P=2(A-6)`

`8=2(10-6)`

`8=2(4)`

`8=8` CHECK