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?
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
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?
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
Thanks! No typo, it must just be another trick up my teacher's sleeve!
To solve this problem, we can create a system of equations based on the given information.
Let's assume the number of ten-dollar bills is represented by 't', the number of five-dollar bills is represented by 'f', and the number of one-dollar bills is represented by 'o'.
We are given the following information:
1. Johnny has 38 bills in total. Therefore, we can write the equation:
t + f + o = 38 -- Equation 1
2. Johnny has twice as many fives as tens. Since the number of fives is twice the number of tens, we can write the equation:
f = 2t -- Equation 2
3. Johnny has three more ones than fives. We can write the equation:
o = f + 3 -- Equation 3
Now, we need to solve this system of equations to find the values of t, f, and o.
To start, we can substitute Equation 2 into Equation 1 and Equation 3:
t + (2t) + o = 38 (substituting f from Equation 2 into Equation 1)
o = (2t) + 3 (substituting f from Equation 2 into Equation 3)
Combining like terms in the first equation:
3t + o = 38 -- Equation 4
Now, we have a system of two equations:
3t + o = 38 -- Equation 4
o = 2t + 3 -- Equation 5
From Equation 5, we can substitute o in Equation 4 with (2t + 3):
3t + 2t + 3 = 38
5t + 3 = 38
5t = 38 - 3
5t = 35
t = 35/5
t = 7
So, Johnny has 7 ten-dollar bills.
Now, let's substitute the value of t into Equation 2 to find the value of f:
f = 2t
f = 2(7)
f = 14
Therefore, Johnny has 14 five-dollar bills.
Finally, let's substitute the value of f into Equation 3 to find the value of o:
o = f + 3
o = 14 + 3
o = 17
Hence, Johnny has 17 one-dollar bills.
In conclusion, Johnny has 7 ten-dollar bills, 14 five-dollar bills, and 17 one-dollar bills.