Jasmin has 50 old coins in a jar and they are either 1cent, 2 centt or 5 cent pieces and their value is $1.20?
If she has twice as many 2-cent coins as 1-cent coints, how many of each type does she have?
Let x = number of 1-cent coins
y = number of 2-cent coins
z = number of 5-cent coins
x + y + z = 50
x + 2y + 5z = 120
y = 2x
Substitute 3rd equation into the first two.
3x + z = 50
5x + 5z = 120
multiply first equation by -5
-15x – 5z = -250
5x + 5z = 120
Add the equations together
-10x = -130
x = 13
y = 2x = 26
13 + 26 + z = 50
39 + z = 50
z = 11
There are 13 1-cent coins, 26 2-cent coins and 11 5-cent coins
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