Question 1045712
Max has a small jar of coins containing pennies, nickels, and dimes. The total number of coins is 44 and the value of the coins is $2.20. If the number of dimes is twice the number of nickels, how many of each type of coin does Max have?
<pre>Ignore the other person's response. No additional info is required.

Let number of pennies, nickels, and dimes be P, N, and D, respectively
Then we get: P + N + D = 44 ------- eq (i) 
Also, .01P + .05N + .1D = 2.2 ----- eq (ii)
And, D = 2N ------ eq (iii)

P + N + 2N = 44 ------- Substituting 2N for D in eq (i)
P + 3N = 44______P = 44 - 3N ------- eq (iv)

.01P + .05N + .1(2N) = 2.2 ------- Substituting 2N for D in eq (ii)
.01P + .05N + .2N = 2.2
.01P + .25N = 2.2 ------ eq (v)

.01(44 - 3N) + .25N = 2.2 ------- Substituting 44 - 3N for P in eq (v) 
.44 - .03N + .25N = 2.2
.44 + .22N = 2.2
.22N = 2.2 - .44
.22N = 1.76
N, or {{{highlight_green(matrix(1,7, Number, of, nickels, "=", 1.76/.22, or, 8))}}}

D = 2(8) ------- Substituting 8 for N in eq (iii)
D, or {{{highlight_green(matrix(1,5, Number, of, dimes, "=", 16))}}}

P = 44 - 3(8) -------- Substituting 8 for N in eq (iv)
P, or {{{highlight_green(matrix(1,7, Number, of, pennies, "=", 44 - 24, or, 20))}}}