Question

I have k quarters, five less quarters than nickels and one more than twice as many dimes as quarters. Find the value of the coins in cents in terms of k.

Answer 1

(35k + 20) cents

Explanation:

First of all, let us have the value of each unit:

1 quarter = 25 cents

1 nickel = 5 cents

1 dime = 10 cents

Given that number of quarter = k

Quarters are 5 lesser than Nickels, so number of nickels = k+5

One more than twice as many dimes as quarters:

k = 2
`*` Number of Dimes + 1

So, number of dimes =
`(1)/(2)(k-1)`

Value of quarters =
`25 * k` cents

Value of nickels =
`5 * (k+5) = (5k+25)\ cents`

Value of dimes =
`(1)/(2)(k-1) * 10 = (5k-5)\ cents`

So, total value of coins =

`25k + 5k +25 +5k-5\\\Rightarrow (35k+20)\ cents`