Question

A cashier put all quarters and dimes received
during a shift into an automated money counter.
The counter sald there were 180 total coins
worth $22.50. How many quarters were there?
A 15 B 30C 90D 150

Answer 1

Option B

There are 30 quarters

Solution:

Let "x" be the number of quarters

Let "y" be the number of dimes

We know that,

Value of 1 quarter = 0.25 dollars

Value of 1 dime = 0.10 dollar

The counter said there were 180 total coins

Therefore,

number of quarters + number of dimes = 180

x + y = 180

y = 180 - x ------- eqn 1

The coins were worth $ 22.50. Therefore, frame a equation as:

number of quarters x Value of 1 quarter + number of dimes x Value of 1 dime = 22.50

$x \times 0.25 + y \times 0.10 = 22.50$

0.25x + 0.1y = 22.50 -------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

0.25x + 0.1(180 - x) = 22.50

0.25x + 18 - 0.1x = 22.50

0.25x - 0.1x = 22.50 - 18

0.15x = 4.5

x = 30

Thus there are 30 quarters