Question

A jar contains n nickels and d dimes. There are 17 coins in the jar, and the total value of the coins is $1.10. How many nickels and how many dimes are in the jar? (Hint: Nickels are worth $0.05 and dimes are worth $0.10.)

Answer 1

Here's what we know:

n + d = 20 (there are a total of 20 nickels and dimes)

.05n + .1d = 1.4 (total change equals $1.40)

There are a couple of ways to solve this. You can go the elimination method by multiplying the second equation by an amount to get rid of a variable, or we can go substitution by isolating a variable in the first equation. I'll go with elimination in this case:

-10(.05n + .1d = 1.4) this will cause the d-variable to equal 0:

n + d = 20

-.5n - d = -14

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.5n = 6

n = 12

Now that we know n, we can solve for d:

12 + d = 20

d = 8

Check:

.05 * 12 + .1 + 8 = 1.4

.6 + .8 = 1.4

1.4 = 1.4

:)