Question

Ben has a collection of quarters and nickels worth $5.35. If the number of nickels is 5 less than twice the number of quarters, find the number of each coin

Answer 1

There are 16 quarters and 27 nickels in the collection.

Step-by-step explanation:

Given,

Worth of nickels and quarters = $5.35 = 5.35*100 = 535 cents

1 quarter = 25 cents

1 nickel = 5 cents

Let,

Number of quarters = x

Number of nickels = y

According to given statement;

25x+5y=535     Eqn 1

y=2x-5               Eqn 2

Putting value of y from Eqn 2 in Eqn 2

$25x+5(2x-5)=535\\25x+10x-25=535\\35x-25=535\\35x=535+25\\35x=560$

Multiplying both sides by 35

$\frac{35x}{35}=\frac{560}{35}\\x=16$

Putting x=16 in Eqn 2

$y=2(16)-5\\y=32-5\\y=27$

There are 16 quarters and 27 nickels in the collection.

Keywords: linear equation, substitution method

Learn more about substitution method at:

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