Question

Write and solve a system of equations that represents each situation. Interpret the solution. 

Neil has a total of twelve $5 and $10 bills in his wallet. He has  5 times as many $10 bills as $5 dollar bills. How many of each does he have?

Answer 1

Let $5 bills be denoted by x and $10 bills be denoted by y.


`x + y = 12 \\ y = 5x \\ \\ x + (5x) = 12 \\ \\ 6x = 12 \\ \\ => x = 2 \\ \\ y = 5x \\ \\ or, y = 5(2) \\ \\ => y = 10`

Thus, there are 2 5$ bills and 10 10$ bills.

Answer 2

x - $5 bills
y - $10 bills

x + y = 12
y = 5x

x + (5x) = 12
6x = 12
x = 2

y = 5(2)
y = 10

10 $10 bills and 2 $5 bills