Posted by Elise on .
Johnny has $147 dollars in ten, five and one dollar bills. He has 38 bills. He has twice as many fives as tens. He has three more ones than fives. How many of each bill does he have?

algebra 
Reiny,
number of tens  x
number of fives  y
number of ones  38xy
10x + 5y + 1(38xy) = 147
9x + 4y = 109
x and y must be integers.
sketch 9x + 4y = 108
xintercept is 12
yintercept is 27
y = (1099x)/4 , we know 0 < x < 12
after some trial and error, x = 9 (only had to try odd x's)
x = 9
y = 7
9 tens
7 fives and
22 ones
check: 90 + 35 + 22 = 147 
algebra 
PsyDAG,
Let x = $5, then x+3 = $1 and .5x = $10. Then:
x + (x+3) + .5x = 38
2.5x = 35
x = 14, x+3 = 17 and .5x = 7
To check:
5*14 + 17 + 10(7) = 147
157 ≠ 147
It doesn't check. Do you have typo? 
oops  algebra 
Reiny,
Should have read the question more carefully, looks like I anticipated the question.
tens  x
fives  2x, it said so
ones  2x+3
10x + 5(2x) + 1(2x+3) = 147
22x = 144
x = 144/22 , which is not a whole number
There is no solution.
I agree with PsyDAG 
algebra 
Elise,
Thanks! No typo, it must just be another trick up my teacher's sleeve!