There are nickels dimes and quarters in a bag The total valu

There are nickels, dimes, and quarters in a bag. The total value of all the coins is $1.65. There is one more nickel then there are quarters, and there are as many dimes as the sum of the number of nickels and quarters. How many coins are there of each kind?

Give your answer in order of nickels, dimes, and quarters.

Solution

1 more nickel than quarter ; dimes = sum of nickels and quarters

Let x = the number of quarters

Then, (x + 1) = the number of nickels

Then, x + (x + 1) or 2x + 1 = the number of dimes.

The value of each is their worth multiplied by the #

This means:

`0.25x + 0.05(x + 1) + 0.10(2x + 1) = 1.65`

Simplify,

`0.5x + 0.15 = 1.65`

`0.5x = 1.5`

`x = 3` represents # of quarters

This means there are 3 quarters, 4 nickels, and 7 dimes