Algebra One Problem

Question

Bella has a stack of 41 bills (ones, fives, and tens) in an envelope. She has 3 less tens than fives and the quantity of ones doubles the number of fives. Write and solve an equation to determine how many of each bill type she has.

Answer 1

T=F-3

W=2F

W+F+T = 41

2F+F + F-3 = 41

4F = 44

F = 44/4 = 11 fives

T=11-3 = 8 tens

W=2(11) = 22 ones

22+11+8 = 41 bills

Answer 2

We have three unknowns: number of ones, fives, and tens

We'll use these variables:

n = number of ones

f = number of fives

t = number of tens

We can make three equations from the information provided

1) n + f + t = 41

2) t = f - 3

3) n = 2f

We'll solve this now. This is pretty hard since we have three equations. To solve it, we'll use substitution and change everything into terms of f. Substitute the second equation in for t in the first equation and substitute the third equation in for n in the first equation. You'll get:

(2f) + f + (f - 3) = 41

Now solve:

4f - 3 = 41

4f = 44

f = 11

Plug this back into the second and third equation to get n and t