SOLUTION: Paul, a french cashier, needs change for his cash register at the Paris Cafe. He needs the following change for 50 Euros: 2 Euro coins, 1 Euro coins and 50 cent coins. He r

Question 1178821: Paul, a french cashier, needs change for his cash register at the Paris Cafe.
He needs the following change for 50 Euros:
2 Euro coins,
1 Euro coins and
50 cent coins.
He receives a total of 44 coins.
The amount of 2 Euro coins and the
amount of 50 cent coins have the same amount of coins.
Find out how many coins of each type he received.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Using formal algebra and a single variable....

Let x = number of 2-Euro coins
Then x = number of 50-cent coins (same as the number of 2-Euro coins)
And 44-2x = number of 1-Euro coins (44, minus the total number of 2-Euro and 50-cent coins)

The total value is 50 Euros:

Solve using basic algebra; I leave that to you.

Informally, using logical reasoning and a bit of mental arithmetic....

Imagine 44 coins, all 1 Euro. That makes a total of 44 Euros, which is 6 Euros short of the actual total.
To increase the value of the total, replace two 1-Euro coins with one 2-Euro coin and one 50-cent coin. That keeps the total number of coins at 44 but increases the total value by 50 cents.
The number of times you need to do that to make the additional 6 Euros is 6/.5 = 12.
So when the total is the correct 50 Euros, you have 12 2-Euro coins, 12 50-cent coins, and 44-24=20 1-Euro coins.

ANSWER:
2-Euro coins: 12
1-Euro coins: 20
50-cent coins: 12

CHECK: 12(2)+20(1)+12(.5) = 24+20+6 = 50

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