SOLUTION: Anna has 12 bills in her wallet, some $5 and some $10. The total value of the bills is $100. How many of each bill does Anna have?

Question 115451: Anna has 12 bills in her wallet, some $5 and some $10. The total value of the bills is $100. How many of each bill does Anna have?
Found 2 solutions by ganesh, aka042:
Answer by ganesh(20) (Show Source): You can put this solution on YOUR website!
Let Anna has x number of $5 bills and y number of $10 bills.
Totally, there are 12 bills.
Therefore, x + y = 12---------(1).
The value of $5 bills = 5*x = 5x.
The value of $10 bills = 10*y = 10y
So, the total value of the bills = 5x + 10y.
It is given that the total value of the bills = $100.
Therefore, 5x + 10y = 100.
That is, x + 2y = 20-----------(2).

Solve (1) and (2).
(1)*2 gives, 2x + 2y = 24------(3)
(2) gives x + 2y = 20-------(2)
(3) - (2) x = 4
Plug in x = 4 in (1), we get y = 8.
So, Anna has 4 bills of $5 and 8 bills of $10

Answer by aka042(26) (Show Source): You can put this solution on YOUR website!
Let's call the number of 5 dollar bills Anna has 'x', and the number of 10 dollar bills Anna has 'y'. Because she has 12 bills in total, we know that . Let's express this in terms of y by subtracting x from both sides: .
Now, we also know that the total value of the bills is $100. Because x is the number of five dollar bills Anna has, 5*x represents the total value of the five dollar bills Anna has. Similarly, 10*y represents the total value of the 10 dollar bills Anna has. Therefore, .
Our first equation tells us that y = 12-x. This means that where ever we see y in the second equation, we can replace it with 12-x. So, . Let's now solve for x by subtracting 120 from both sides and then dividing through by -5: . => . (=> means "implies that"). So x = 4, which means Anna has 4 five dollar bills.
Finally, let's return to our initial equation that y = 12 -x. We know x to be 4, so , which means Anna has 8 ten-dollar bills.
Therefore we conclude that Anna has 4 five-dollar bills and 8 ten-dollar bills.
Let's just check to make sure. The question states that she has 12 bills in her wallet. Well 4 + 8 = 12, so that works out. It also states that the total value of the bills is $100. We say that Anna has 4 five-dollar bills, which totals 20 dollars, and 8 ten-dollar bills, which totals 80 dollars. 80 dollars + 20 dollars = 100 dollars, so that works also.
Therefore, Anna has 4 five-dollar bills and 8 ten-dollar bills.
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