Question 1178821
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Using formal algebra and a single variable....<br>
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)<br>
The total value is 50 Euros:<br>
{{{2(x)+.5(x)+1(44-2x) = 50}}}<br>
Solve using basic algebra; I leave that to you.<br>
Informally, using logical reasoning and a bit of mental arithmetic....<br>
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.<br>
ANSWER:
2-Euro coins: 12
1-Euro coins: 20
50-cent coins: 12<br>
CHECK: 12(2)+20(1)+12(.5) = 24+20+6 = 50<br>