Call the number of hours babysitting [tex]B[/tex] and the number of hours walking dogs [tex]D[/tex].
We know that she earns $6/hr for babysitting or [tex]6B[/tex], and $5/hr walking dogs or [tex]5D[/tex]. We also know the total money is $43 and the total time is 8hours. Therefore:
[tex]B+D=8[/tex]
[tex]6B+5D=43[/tex]
To solve: First rearrange equation 1 to solve for either [tex]B[/tex] or [tex]D[/tex] (doesn't matter which, I'll use [tex]B[/tex]):
[tex]B=8-D[/tex]
Now substitute into equation 2:
[tex]6(8-D)+5D=43[/tex]
and solve for [tex]D[/tex]
[tex]48-6D+5D=43[/tex]
[tex]-D=-5[/tex]
[tex]D=5[/tex]
Now backsubstitute to solve for [tex]B[/tex]:
[tex]B=8-D[/tex]
[tex]B=8-5[/tex]
[tex]B=3[/tex]
She babysat for 3 hours and walked dogs for 5.
To check our work:
[tex]6B+5D=43[/tex]
[tex]6(3)+5(5)=43[/tex]
[tex]18+25=43[/tex]
[tex]43=43[/tex] CHECKS
