Select the equation that solves this problem:

Eight coins (dimes and nickels) are worth 60 cents. How many dimes are
there?
a. 10d + 25(11 - d) = 170
b. 10d + 25(8 - d) = 170
c. 10d + 5(8 - d) = 60
d. 10d + 5(11 - d) = 60

C.

d = the number of dimes, while 8-d equals the numbers of nickels, if you multiply the number of each coins by their value ( 10 cents or 5 cents ) and add them, you should get 60

A nickel is worth 5 cents and a dime is worth 10 cents.

n = numbers of a nickels

d = numbers of a dimes

n + d = 8

n = 8 - d

Value of money :

10 ¢ * d + 5 ¢ * n = 60 ¢

10 d + 5 n = 60

10 d + 5 ( 8 - d ) = 60

Equation c.

10 d + 5 ( 8 - d ) = 60

10 d + 5 * 8 + 5 * ( - d ) = 60

10 d + 40 - 5 d = 60

5 d + 40 = 60

5 d = 60 - 40

5 d = 20 Divide both sides by 5

d = 20 / 5

d = 4

n = 8 - d = 8 - 4 = 4

4 dimes and 4 nickels

4 * 10 ¢ + 4 * 5 ¢ =

40 ¢ + 20 ¢ = 60 ¢

To solve this problem, we can set up an equation to represent the given information. Let's use d to represent the number of dimes.

Since each dime is worth 10 cents, the value of all the dimes is 10d cents. And since each nickel is worth 5 cents, the value of all the nickels is 5(8-d) cents.

The total value of the coins is 60 cents.

Therefore, the equation that represents this problem is: 10d + 5(8 - d) = 60.

Thus, the answer is option c. 10d + 5(8 - d) = 60.

To solve this problem, we need to set up an equation based on the given information. We are given that there are eight coins, which are either dimes or nickels, and the total value of these coins is 60 cents.

Let's break down the problem step by step:

1. Let's assume there are d dimes in the collection. Since there are eight coins in total, the number of nickels would be (8 - d).

2. The value of each dime is 10 cents, so the total value of the dimes would be 10d cents.

3. The value of each nickel is 5 cents, so the total value of the nickels would be 5(8 - d) cents.

4. The sum of the values of the dimes and nickels should be equal to 60 cents. Therefore, we can set up the following equation:

10d + 5(8 - d) = 60

Now let's compare this equation with the given options:

a. 10d + 25(11 - d) = 170
b. 10d + 25(8 - d) = 170
c. 10d + 5(8 - d) = 60
d. 10d + 5(11 - d) = 60

The equation that matches the setup we derived is option c:

10d + 5(8 - d) = 60

Therefore, the correct equation that solves this problem is option c.