Question 482220
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Algebraically....<br>
x+y=50  the number of coins is 50
5x+1y=130  the value of the coins is 130 pesos<br>
The difference between the two equations is 4x=80, leading to x=20; that makes y=50-20=30<br>
ANSWER: 20 5-peso coins and 30 1-peso coins<br>
CHECK: 20(5)+30(1)=100+30=130<br>
Informally (if an algebraic solution is not required, and if the speed of getting the answer is important)....<br>
(1) imagine starting with all 50 coins being 1-peso coins; that would make the total 50 pesos, which is 80 pesos short of the actual total.
(2) exchanging a 1-peso coin for a 5-peso coin keeps the total number of coins the same but increases the total value by 5-1=4 pesos.
(3) 80/4 means there have to be 20 5-peso coins; and that means 30 1-peso coins<br>
The words of explanation make this informal solution longer than the formal algebraic solution.  But without all the words, here are the complete calculations for this method:<br>
50(1)=50
130-50=80
80/4=20
50-20=30<br>