Question 1034271


A collection of nickels, dimes, and quarters consist of 60 coins with a total of $6.50. If there are 3 times as many dimes as quarters, find the number of each type of coins.
<pre>Let number of nickels and quarters, N, and Q, respectively
Then number of dimes = 3Q
We then get: N + Q + 3Q = 60_____N + 4Q = 60 ------- eq (i)
Also, .05N + .25Q + .1(3Q) = 6.5____.05N + .25Q + .3Q = 6.5____.05N + .55Q = 6.5 ---- eq (ii)
- .05N - .2Q = - 3 ------- Multiplying eq (i) by – .05 ------- eq (iii)
.35Q = 3.5 ------- Adding eqs (iii) & (ii)
Q, or number of quarters = {{{3.5/.35}}}, or {{{highlight_green(10)}}}
N + 4(10) = 60 --------- Substituting 10 for Q in eq (i)
N + 40 = 60
N, or number of nickels = 60 – 40, or {{{highlight_green(20)}}}
Number of dimes: 3(10), or {{{highlight_green(30)}}}