Vern has a collection of pennies, nickels, and dimes. The ratio of the number of pennies to the number of nickels is 9:2, and the ratio of the number of nickels to the number of dimes is 3:4. If the total worth of Vern's collection is $\$10.96,$ then how many coins do they have in total?
Let the number of pennies, nickels, and dimes be 9x,2x, and 4x respectively. Since one penny is worth $0.01, one nickel is worth $0.05, and one dime is worth $0.10, the total value of the collection is \begin{align*} 0.01(9x) + 0.05(2x) + 0.10(4x) &= 1.09x. \ \end{align*}We are also given that the total worth of the collection is $10.96, so we have [1.09x = 10.96.]Solving for x, we find x=100. Therefore, the total number of coins is 9x+2x+4x=152.
P/N==9/2......................................(1)
N/D==3/4.....................................(2)
0.01P + 0.05N + 0.10D==10.96...(3), solve for P, N, D
P==216 pennies
N==48 Nickels
D==64 Dimes
Total ==216 + 48 + 64 ==328 coins
Check: [0.01 x 216] + [0.05 x 48] + [0.10 x 64]==$2.16 + $2.40 + $6.40 ==$10.96
