Respuesta :

twvogels
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 [tex] A+P=18 [/tex].

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

Now we can substitute the second equation into the first:
[tex]A+P=18[/tex]
[tex]A+(2(A-6))=18[/tex]

And solve for A:
[tex]A+2A-12=18[/tex]
[tex]3A=30[/tex]
[tex]A=10[/tex]

Alice hit 10 home runs.

Now we can plug this known value into the first equation and solve for P:
[tex]A+P=18[/tex]
[tex]10+P=18[/tex]
[tex]P=8[/tex]

Peter hit 8 home runs.

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

[tex]P=2(A-6)[/tex]
[tex]8=2(10-6)[/tex]
[tex]8=2(4)[/tex]
[tex]8=8[/tex] CHECK


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