How many 10-bills does River have, and how many 5$ bills?

Question

River has been saving some money. Last night she counted 94 bills - $1’s, $5’s and $10’s- with a total value of $598. She has twice as many $5-bills as she has $1-bills . How many $10-bills does she have?

Answer 1

A substitution will work here.

We know we have 94 bills with 5's being twice as many as 1's, so the 10's would be what is left over.

The 10's would be equal to 94 minus the 1's plus the 5's. The combination of these quantities times their values adds up to $598.

For the 94 bills let

1's = x

5's = 2x

Since x +2x = 3x = 1's plus 5's

10's = 94 -3x

For the total value we have

x + 5(2x) + 10(94 - 3x) = 598

x + 10x + 940 -30x = 598

11x - 30x + 940 = 598

940 -19x = 598

We can add 19x to both sides of the equation then subtract 598 from both sides of the equation

940 - 598 = 19x

342 = 19x

Divide both sides of the equation by 19

342/19 = x

18 = x

Going back to the original substitutions

We have

x = 18 dollar bills

2x = 36 Five dollar bills

94-3x = 94 - 54 = 40 Ten dollar bills

Checking our total value we

18 + 5(36) + 10(40)

18 + 180 + 400 = 598

I hope this helps please send me a message if you have any questions.