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 -- 38-x-y
10x + 5y + 1(38-x-y) = 147
9x + 4y = 109
x and y must be integers.
sketch 9x + 4y = 108
x-intercept is 12
y-intercept is 27
y = (109-9x)/4 , we know 0 < x < 12
after some trial and error, x = 9 (only had to try odd x's)
x = 9
y = 7
7 fives and
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
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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