# algebra

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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 -

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

9 tens
7 fives and
22 ones

check: 90 + 35 + 22 = 147

• algebra -

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 -

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 -

Thanks! No typo, it must just be another trick up my teacher's sleeve!