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 to

Question

3 years ago

6

gether exceed the number of quarters by 19. How many quarters are in the jar?

1 answer:

ivolga24 [154] · Answer 1 · 2022-06-26T02:34:09+03:00

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

$(z+19)+z=45\\z+19+z=45\\2z=45-19\\2z=26$

Dividing both sides by 2

$\frac{2z}{2}=\frac{26}{2}\\z=13$

There are 13 quarters in the jar.

Keywords: linear equation, substitution method

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