math word problem

Question

1. Ms. Fraser has 12 coins in her pocket which are dimes and nickels. If she has 85 cents in all, how many of each coin does she have? Show all of your work on your notebook paper.*

Answer 1

Let's use the variable d to represent the NUMBER of dimes and the variable n to represent the NUMBER of nickels.

Since there are total of 12 coins, we can write the following equation:

d + n = 12

The coins are worth $0.85 in total and we can write the following equation to show this:

0.10d + 0.05n = 0.85

Now we have two equations with two unknowns that we can solve using substitution or elimination. Let's try substitution:

The first equation can be rewritten to create an expression for n:

d + n = 12

n = 12 - d

Now we can substitute 12 - d for n in the second equation and determine the number of dimes, d:

0.10d + 0.05n = 0.85

0.10d + 0.05(12 - d) = 0.85

0.10d + 0.6 - 0.05d = 0.85

0.05d + 0.6 = 0.85

0.05d + 0.6 - 0.6 = 0.85 - 0.6

0.05d = 0.25

0.05d / 0.05 = 0.25/0.05

d = 5

There are 5 dimes. Since there are 5 dimes, there will be 7 nickels.

NOTE: 5 dimes is worth 50 cents and 7 nickels is worth 35 cents: Total is $0.85