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A jar of 45 coins consists only of nickels, dimes, and quarters, with a face value of $5.90. The numbers of nickels and dimes together exceed the number of quarters by 19. How many quarters are in the jar?

Respuesta :

absor201

There are 13 quarters in the jar.

Step-by-step explanation:

Given,

Number of coins in jar = 45 coins

Worth of coins = $5.90 = 5.90*100 = 590 cents

1 nickel = 5 cents

1 dime = 10 cents

1 quarter = 25 cents

Let,

Number of nickels = x

Number of dimes = y

Number of quarters = z

According to given statement;

x+y+z=45       Eqn 1

5x+10y+25z=590    Eqn 2

x+y=z+19          Eqn 3

Putting value of x+y from Eqn 3 in Eqn 2

[tex](z+19)+z=45\\z+19+z=45\\2z=45-19\\2z=26[/tex]

Dividing both sides by 2

[tex]\frac{2z}{2}=\frac{26}{2}\\z=13[/tex]

There are 13 quarters in the jar.

Keywords: linear equation, substitution method

Learn more about substitution method at:

  • brainly.com/question/1096947
  • brainly.com/question/11018983

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