Question

Louis has three more quaters than dimes in his pocket. for a total of $1.80. Which equation could've used to determine the number of dimes, x, in his pocket?
A. 0.10(x+3)+0.25x=$1.80
B.0.10x+0.25(x+3) = $1.80
C. 0.10(3x)+0.25x=$1.80
D. 0.10x+0.25(3x)=$1.80

Answer 1

To determine the correct equation to represent the situation described, let's analyze the problem step by step.

1. **Identify the Variables**: We are told that Louis has dimes and quarters. Let \( x \) represent the number of dimes he has.

2. **Quarters**: The problem states that Louis has three more quarters than dimes. Therefore, the number of quarters he has is \( x + 3 \).

3. **Value of Dimes and Quarters**:
- The value of dimes in dollars: \( 0.10x \) (since each dime is worth 0.10 dollars).
- The value of quarters in dollars: \( 0.25(x + 3) \) (since each quarter is worth 0.25 dollars).

4. **Total Value**: The total value of all the coins is $1.80, which can be represented by the equation:
\[
0.10x + 0.25(x + 3) = 1.80
\]

Now, looking at the options given, the correct equation based on our analysis is:

**B. \( 0.10x + 0.25(x + 3) = 1.80 \)**

This matches the formulation we derived. Therefore, the correct choice is option B.