Sally has seven times as many dimes as nickels. Their value is $3.00. How many nickels does she have?

Answer 1

Let's let D be the number of dimes she has and N be the number of nickels.

We then have the following equations:

Equation (a): D = 7N

Equation (b): $0.10D + $0.05N = $3.00

First let's use the information from equation (a) to solve for the number of nickels in equation (b):

$0.10(7N) + $0.05N = $3.00

This gives us:

$0.70N + $0.05N = $3.00

Combining terms on the left hand side gives us:

$0.75N = $3.00

Let's divide both sides by $0.75:

$0.75N / $0.75 = $3.00 / $0.75

Or equivalently:

N = 4

Plugging N = 4 into equation (a) then gives us:

D = 7(4) = 28

So Sally has 28 dimes and 4 nickels.

To double-check our answer, let's make sure this works for equation (b):

28($0.10) + 4 ($0.05) = $2.80 + $0.20 = $3.00

which confirms that she has 28 dimes and 4 nickels.