SOLUTION: A change machine at an arcade gives change for $1 bills and $5 bills. If during a particular day, 200 bills were inserted into the machine and the total vaule was $300, how many $1

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Question 847420: A change machine at an arcade gives change for $1 bills and $5 bills. If during a particular day, 200 bills were inserted into the machine and the total vaule was $300, how many $1 bills were inserted into the machine?
A) 25
B)75
C)125
D)175
Can you please show me how to solve it? I already know the answer is D- 175 but I just don't know how to get that.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Let
x = number of $1 bills
y = number of $5 bills

There are 200 bills of just $1 and $5 bills. So the two must add to 200

x + y = 200

Solve for y to get y = 200 - x

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If you have x $1 bills and y $5 bills, then you'll have a total of x + 5y dollars. But we know this total is also equal to $300, so

x + 5y = 300

Replace each copy of y with 200 - x (since above we know that y = 200 - x) to get

x + 5y = 300

x + 5(y) = 300

x + 5(200 - x) = 300

x + 5(200 - x) = 300

Notice how y is completely gone now. Now solve for x

x + 5(200 - x) = 300

x + 5(200) + 5(-x) = 300

x + 1000 - 5x = 300

-4x + 1000 = 300

-4x = 300 - 1000

-4x = -700

x = -700/(-4)

x = 175

We could stop here, but let's keep going to find y

y = 200 - x

y = 200 - 175

y = 25

This bit is extra, but it helps to know how to find it (if asked).

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Answer:

Since x = 175, this means that there are 175 one dollar bills.

Note: if you forget what x is, look back up at the definitions above. This is why it helps to set these up first.