4. The total value of the $1 bills and $5 bills in a cash box is $124. There are 8 more $5 bills than $1 bills. How many of each are there?

Answer 1

pretend $1 is x
and $5 is y

x+8=y *bc you have to add 8 $1 to
have the same number of $1 as $5

1x+5y=124 *this is basically saying that there is an "x" number of $1 bill plus a "y" number of $5 will get u $124

now use elimination:
since y=x+8 plug "x+8" as "y" in the other equation

1x+5(x+8)=124
1x+5x+40=124 *distribute
6x=84
x=14

now plug "x" into the first equation to find y:
x+8=y
14+8=y
y=22

this means that 14 $1 and 22 $5 will get you $124

now check your answer:
14+8=22 *correct
and
1(14)+5(22)=124 *correct