Question

7. A vending machine only accepts dimes and quarters. There are 85 coins
in the machine with a total value of $16.75. How many of each coin are in
the machine?

Answer 1

There are 55 quarters and 30 dimes in the machine.

Step-by-step explanation:

Total coins = 85

Total amount = $16.75 = 16.75*100 = 1675 cents

1 quarter = 25 cents

1 dime = 10 cents

According to given statement;

x+y=85    Eqn 1

25x+10y=1675   Eqn 2

Multiplying Eqn 1 by 10

$10(x+y=85)\\10x+10y=850\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(25x+10y)-(10x+10y)=1675-850\\25x+10y-10x-10y=825\\15x=825$

Dividing both sides by 15

$\frac{15x}{15}=\frac{825}{15}\\x=55$

Putting in Eqn 1;

$55+y=85\\y=85-55\\y=30$

There are 55 quarters and 30 dimes in the machine.

Keywords: linear equation, subtraction

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