A jar contains 60 nickels and dimes worth 530 How many of ea

A jar contains 60 nickels and dimes worth $5.30. How many of each kind of coin are in the jar?

Solution

given

x+y=60 --------------------------------------1

x($0.05) +y($0.1) = $5.3

0.05x+0.1y=5.3

multiplying it with 20 on both sides (in order to make x coefficient 1)

x+2y=106 ---------------------------------------------------2

Now subtract equation 1 from 2

x+2y=106

-(x+y=60)

-------------------------------------------------

x-x+2y-y=106-60

y=46

substitute y in x+y=60

x+46=60

so x=14