Dollar bills and system of two linear equations

by Kendall Whiteside
(Happy Valley, Oregon)

“A student has some $1 bills and $5 bills in his wallet. He has a total of 15 bills that are worth $47. How many of each type of bill does he have? ”

Let x be the number of $1 bills and y be the number of $5 bills.

The number of $1 bills plus the number of $5 bills equal 15 or x + y = 15

Worth of $1 bills plus worth of $5 bills = $47 or 1x + 5y = 47


Therefore, just solve the system of equations below.

x + y = 15 (1)

x + 5y = 47 (2)


(2) minus (1) will give 4y = 32

y = 8 since 4 × 8 = 32

x + 8 = 15

x = 7

The student has seven $1 bills and eight $5 bills.