Posted by Elise on Monday, November 12, 2012 at 12:48pm.
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, Monday, November 12, 2012 at 1:02pm
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, Monday, November 12, 2012 at 1:09pm
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, Monday, November 12, 2012 at 1:21pm
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, Monday, November 12, 2012 at 8:40pm
Thanks! No typo, it must just be another trick up my teacher's sleeve!
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