Question 1046005

A collection of 24 coins, consisting of nickels, dimes, and quarters, has a value of $3.40. If there are twice as many quarters as nickels, and one-third as many nickels as dimes, how many coins of each kind are there?
<pre>Let the number of nickels, dimes, and quarters, be N, D, and Q, respectively
Then we get: N + D + Q = 24 -------- eq (i)
Also, Q = 2N
As there are {{{1/3}}} as many nickels as dimes, it follows that: D = 3N
N + 3N + 2N = 24 ------ Substituting 2N for Q, and 3N for D in eq (i)
6N = 24
N, or number of nickels = {{{24/6}}}, or {{{highlight_green(4)}}}
Number of dimes: 3(4), or {{{highlight_green(12)}}}
Number of quarters: 2(4), or {{{highlight_green(8)}}}
As seen, the value of these 24 coins was not needed. In other words, it was totally unnecessary to include it!