Question

The twenty-six coins in my pocket are all dollar coins and quarters, and they add up to seventeen dollars in value. How many dollar coins and how many quarters are in my pocket?

Answer 1

Currency such as dollars can come in various forms such as dimes, quarters, pennies, and nickels.

The number of quarter coins is 12 and the number of dollar coins is 14 coins.

Let's represent:

The number of 1 dollar coin = d

The number of 1 quarter coin = q

The twenty-six coins in my pocket are all dollar coins and quarters. The algebraic equation for this statement above is =

d + q = 26 ........ Equation 1

Making d the subject of the formula

d = 26 - q

1 dollar coin = $1

1 quarter = $0.25

The value of the dollar and nickel coins is seventeen dollars. The algebraic expression for this statement is :

$1 x d + $0.25 x q = 17

d + 0.25q = 17.................Equation 2

Substitute 26 - q for d in Equation 2

26 - q + 0.25q = 17

Collecting like terms

26 - 17 = q - 0.25q

9 = 0.75q

Divide both sides by 0.75

9/0.75 = 0.75q/0.75

q = 12 coins

Solving for number of dollar coins

d = 26 - q

q = 12

d = 26 - 12

d = 14 coins

Therefore, the number of quarter coins is 12 and the number of dollar coins is 14 coins.

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