Question

1. a collection of dimes and nickels has a total value of two dollars and contains 31 coins. how many dimes are there in the collection? 7 dimes 11 dimes 9 dimes 13 dimes

Explanation:

Step1: Define Variables

Let \( d \) be the number of dimes and \( n \) be the number of nickels. We know two equations: \( d + n = 31 \) (total coins) and \( 0.10d + 0.05n = 2.00 \) (total value in dollars). From the first equation, \( n = 31 - d \).

Step2: Substitute into Value Equation

Substitute \( n = 31 - d \) into \( 0.10d + 0.05n = 2.00 \):
\( 0.10d + 0.05(31 - d) = 2.00 \)

Step3: Solve for \( d \)

Expand: \( 0.10d + 1.55 - 0.05d = 2.00 \)
Simplify: \( 0.05d + 1.55 = 2.00 \)
Subtract 1.55: \( 0.05d = 0.45 \)
Divide by 0.05: \( d = \frac{0.45}{0.05} = 9 \)

Answer:

9 dimes (corresponding to the option "9 dimes")