Coin Problem including dimes, quarters and nickels

Question

A piggy bank has only nickels, dimes and

quarters in it, totaling $7.65. The number of

quarters is seven more than twice the number of

nickels, and the number of dimes is two thirds

the difference of the number of nickels and four.

Find the number of nickels, dimes and quarters.

Answer 1

Let x = number of nickels

Then number of quarters = 2x + 7

number of dimes = (2/3)(x - 4)

0.05x + 0.25(2x + 7) + 0.10[(2/3)(x - 4)] = 7.65

0.05x + 0.50x + 7/4 + (1/15)x - (4/15) = 7.65

0.61666666x = 6.16666666

x = 10

There are 10 nickels, 4 dimes, and 27 quarters.

Answer 2

q*(7+2n)+d*(.66(n-4))+n=7.65

7q+2nq+ d*(.66n-2.66)+n=7.65

7q+2nq+ .66dn-2.66d +n=7.65