Question

Karen makes $5 per hour for babysitting and $12 per hour giving music lessons. One week she worked a total of 18 hours and made 139$ that day. How many hours did she spend babysitting ?

Answer 1

B = hours babysitting
m = hours giving music lessons

so... whatever "b" and "m" are, their sum for that week was 18
thus
b + m = 18

now, money wise, she makes $5 for "b" and that is, she made 5*b or 5b that week
for "m", she makes $12, so for that week she made 12*m or 12m

whatever "b" and "m" are
thus

5b + 12m = 139

now $\bf \begin{cases} b+m=18\to \boxed{m}=18-b\\\\ 5b+12m=139\\ ----------\\ 5b+12\left( \boxed{18-b}\right)=139 \end{cases}$

solve for "b", to see how many hours she spent babysitting