systems of equations, word problem

Question

Sam has 15 coins, all nickels an dimes, with a total value of  .90 cents.

How many of each coin does he have?( let d = the number of dimes and n = the number of nickels)

 A. write a system of equations to model the problem

B.solve the system

 C. state your answer with the proper label or labels.

Answer 1

1).  n + d = 15

2).  .05n + .10d = .90

use equation 1) and solve for n

1a).  n = 15 - d

substitute into 2).

.05(15 - d) + .10d = .90

divide all terms by .05

15 - d + 2d = 18

d = 3

substitute this into equation 1).

n + 3 = 15

n = 12

he had 12 nickels and 3 dimes.

check:

12*.05 + 3*.10 = .60 + .30 = .90  it works.