Question

Elizabeth has 144 coins. Of the coins, 3/12 are nickels, 3/12 are dimes, and the rest are quarters. What is the ratio of Elizabeth’s nickels to dimes to quarters?

Answer 1

`\huge\boxed{\sf 1 : 1 : 2}`

Explanation:

Total coins = 144

Nickels:

= 3/12 of total

Key: "of" means "to multiply".

`\displaystyle =(3)/(12) * 144\\\\= (3 * 144)/(12) \\\\= (432)/(12) \\\\= 36\ nickels`

Dimes:

Since the fraction of dimes and nickels is the same, so:

Dimes = 36

Quarters:

The rest of the coins have to be quarters.

So,

= 144 - 36 - 36

= 72 quarters

The ratio of nickels to dimes to quarters:

= 36 : 36 : 72

Highest common factor = 36.

So, divide by 36.

= 36/36 : 36/36 : 72/36

= 1 : 1 : 2

`\rule[225]{225}{2}`