The number of each kind of coin, Sonali has as 22 quarters, 19 nickels and 26 dimes in his collection.
What is quarter and nickel?
The quarter and nickel are the coins having keeping some value of dollar.
- Quarter-In one quarter there is total 25 cents or 0.25 dollars.
- Nickel-In one nickel there is total 5 cents or 0.05 dollars.
Let Sonali has x quarters, y nickels and z dimes. Sonali has 67 coins in his collection. Thus,
[tex]x+y+z=67[/tex] ......1
There are three more quarters than nickels. Thus,
[tex]x=y+3[/tex] .....2
There are seven fewer nickels than dimes.
[tex]y=z-7\\z=y+7[/tex] .....3
Put the value of x and z from equation 2 and 3 in the equation 1. Thus,
[tex](y+3)+y+(y+7)=67\\3y=67-3-7\\y=\dfrac{57}{3}\\y=19[/tex]
Put this value in equation 2,
[tex]x=19+3\\x=22[/tex]
Again, put the value of x in equation 3,
[tex]z=19+7\\z=26[/tex]
Hence, the number of each kind of coin, Sonali has as 22 quarters, 19 nickels and 26 dimes in his collection.
Learn more about the quarter and nickel here;
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