Graham was working a booth at a carnival that sold various food items. at the end of his shift he was counting up the amount of cash he collected. all of the money he had was either $1 bills or $5 bills. if he had a total of 124 bills that was worth $300, set up and solve a system of equations to determine how many of each type of bill he had.

equations:

1x + 5y = 300

x + y = 124

solve:

1x + 5y = 300

subtract 1x

5y = -1x + 300

divide the right side by 5

y = -1/5x + 60

solve:

x + y = 124

subtract x

y = -x + 124

so:

-x +124 = -1/5x + 60

add 1/5x to both sides to cancel it out on the right side

-4/5x + 124 = 60

subtract 124 from both sides to cancel it out on the left side

-4/5x = -64

divide -4/5 by -64

x = 80

then:

substitute 80 for x in one of the equations to get y = 44

in conclusion:

there were 80 $1 bills and 44 $5 bills