Question

A bag contains 3 types of coins: nickels (worth 5 cents each), dimes (worth 10 cents each)
and quarters (worth 25 cents each) in the ratio 5:3 : 2. If the total value of the dimes is
50 cents more than that of the nickels, then how many quarters does the bag contain?​

Answer 1

Given:

• The ratio of the number of coins; nickels : dimes : quarters = 5 : 3 : 2
• Total value of dimes is 50 cents more than that of nickels.

To find: How many quarters does the bag contain?

Solution:

Given, the ratio of the number of coins;

nickels : dimes : quarters = 5 : 3 : 2

Let, x be the common multiple.

Then,

• number of nickels = 5x
• number of dimes = 3x
• number of quarters = 2x

We find:

• value of 5x nickels = 5 * 5x cents = 25x cents
• value of 3x dimes = 10 * 3x cents = 30x cents
• value of 2x quarters = 25 * 2x = 50x cents

By the given condition, total value of dimes is 50 cents more than that of nickels. Then,

30x = 25x + 50

or, 30x - 25x = 50

or, 5x = 50

or, x = 10

Therefore the number of quarters in the bag is (2 * 10) = 20.