https://file.aiquickdraw.com/mathbot/file/1730003842762xav8rb4f.jpg

Let's solve this step-by-step.

1. **Define Variables**:
   - Let $ x $ be the number of 5-cent coins.
   - Since the man has twice as many 10-cent coins, he has $ 2x $ 10-cent coins.

2. **Set Up the Equation**:
   - The value of the 5-cent coins is $ 5x $ cents.
   - The value of the 10-cent coins is $ 10 \times 2x = 20x $ cents.
   - The total value of all coins is $1.75, which is 175 cents.

3. **Form the Equation**:
   \[
   5x + 20x = 175
   \]

4. **Solve the Equation**:
   \[
   25x = 175
   \]
   \[
   x = \frac{175}{25} = 7
   \]

5. **Interpret the Solution**:
   - $ x = 7 $, so there are 7 five-cent coins.
   - The number of 10-cent coins is $ 2x = 2 \times 7 = 14 $.

### Answer:
The man has 7 five-cent coins and 14 ten-cent coins.

Would you like further details on this solution, or do you have any questions?

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Here are some related questions to consider:
1. How would the solution change if the total value was different, say $2.00?
2. What if he had three times as many ten-cent coins as five-cent coins?
3. How would you solve it if he had a different ratio between the two types of coins?
4. Can you solve this problem using a system of equations approach?
5. What if there were also 25-cent coins included in the problem?

**Tip**: Converting dollars to cents can simplify the math, as it eliminates decimal points.

A man has a certain number of five-cent coins and has twice as many ten-cent coins. If the total value of the coins is $1.75, find the number of each type of coin.

Learn how to solve a coin problem involving 5-cent and 10-cent coins, with a total value of $1.75. This solution uses linear equations to find the number of each type of coin. Suitable for students in Grades 6-8.

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