Question

Danielle has $6.65 worth of change in nickels and dimes. If she has 5 times as many nickels as dimes, how many of each type of coin does she have?

Answer 1

95 nickels 19 dimes

Explanation:

d=dimes

5d=nickels

0.05(5d) + 0.10(d) = 6.65

0.25d + 0.10d = 6.65

0.35d=6.65

Divide by 0.35

d= 19 (19 coins)

19 dimes =$1.9

6.65-1.9= $4.75

Nickels=$4.75

4.75/0.05 = 95 coins

19*5=95

114 coins in total

19*0.10 = 1.9

95*0.05=4.74

4.75+1.9= 6.65

Answer 2

There are 19 dimes and 95 nickels

Explanation:

Represent the numbers of nickels and dimes by n and d. Then n = 5d.

The value of the nickels is $0.05n and that of the dimes is $0.10d. Together these two amounts come to $6.65:

$0.05n + $0.10d = $6.65.

But n = 5d.

Substituting 5d for n, we get:

$0.05(5d) + $0.10d = $6.65

Combining the two terms on the left, we get:

0.25d + 0.10d = 6.65, or

0.35d = 6.65.

Solving for d, we get d = 6.65/0.35, or d = 19. Since n = 5d, n = 5(19) = 95.

There are 19 dimes and 95 nickels.