Linear equation

Question

Piggy bank containa 27 coins consisting of nickels (×), dimes (y), and quarters (z). The total amount of money in the bank is $5.05. If the number of quarters is twice the number of nickels and dimes. Find the number of each type of coin in the bank

Answer 1

x+y+z=27

.05x+.10y+.25z=5.05

z = 2(x+y) =2x+2y

Substituting in for z for the first equation

x+y+2x+2y=27

3x+3y=27

x+y=9

y=9-x

Substituting for y and z into the second equation

.05x+.10(9-x)+.25(2x+2(9-x))=5.05

.05x+.9-0.1x+.50x+.50(9-x) = 5.05

.05x +.9-0.1x+.5x+4.5-.5x = 5.05

-0.05x= 5.05-5.40 =-0.35

x=7

y=9-7=2

z=14+4=18

7 nickels

2 dimes

18 quarters