debra saved only dimes and nickels in her bank when she last counted the coins she noticed there were twice as many dimes as nickels she had $4.75 in her bank how many dimes did she have in her bank?

a. 38
b. 24
c. 12
d. 19

A. 38

Step-by-step explanation:

Let d = number of dimes.

Let n = number of nickels.

First equation:

There are twice as many dimes as nickels. The number of dimes is 2 times the number of nickels. The first equation is:

d = 2n

Second equation:

The value of a dime is $0.10. The value of a nickel is $0.05. The value of d number of dimes is 0.1d. The value of n number of nickels is 0.05n. The total value of d dimes and n nickels is 0.1d + 0.05n. We are told the total value of her dimes and nickels is $4.75. That gives us the second equation:

0.1d + 0.05n = 4.75

We have two equations and two unknowns, so we can answer this question by solving a system of two equations in two unknowns.

d = 2n

0.1d + 0.05n = 4.75

We will use the substitution method.

Since d = 2n, replace d in the second equation with 2n.

0.1(2n) + 0.05n = 4.75

0.2n + 0.05n = 4.75

0.25n = 4.75

n = 4.75/0.25

n = 19

Now that we know the number of nickels, we use the equation d = 2n to find the number of dimes.

d = 2n

d = 2 * 19

d = 38

Debra had 38 dimes.