Susan paid for her library fine with 21 coins consisting of nickels and dimes. If the fine was ?$1.65?, how many coins were? nickels?

Question

I know the general concept i think, but cant figure this one out  

Answer 1

Here's what we know:

n + d = 21 (there are a total of 21 nickels and dimes)

.05n + .1d = 1.65 (the nickels and dimes total $1.65)

We can isolate a variable and use the substitution method:

n = 21 - d

 

Now that we have a value, let's plug it in:

.05(21 - d) + .1d = 1.65

Distribute:

1.05 - .05d + .1d = 1.65

combine like terms:

.05d + 1.05 = 1.65

Subtract 1.05 from both sides:

.05d = .6

Divide both sides by .05:

d = 12

 

n = 21 - 12

n = 9

 

check:

.05 * 9 + .1 * 12 = 1.65

.45 + 1.2 = 1.65

1.65 = 1.65