Sasa had some 20-cent and 50-cent coins. Let x be the total number of coins. Then, 7/8 x were 20-cent coins, and the rest, 1 - 7/8 = 1/8 x, were 50-cent coins. After Sasa spent $72.50 worth of 50-cent coins, which is equivalent to 72.50 / 0.50 = 145 50-cent coins, and 5/7 of the 20-cent coins, she had 2/7 x coins left. Find the total amount of money Sasa left.

Let's break down the problem step-by-step.

1. **Initial Coins:**
   - Let $ x $ be the total number of coins.
   - $ \frac{7}{8}x $ were 20-cent coins.
   - $ \frac{1}{8}x $ were 50-cent coins.

2. **Spending the Coins:**
   - Sasa spent $72.50 worth of 50-cent coins:
     \[
     \frac{72.50}{0.50} = 145 \quad \text{(50-cent coins)}.
     \]
   - The initial number of 50-cent coins was $ \frac{1}{8}x $. Therefore,
     \[
     \frac{1}{8}x - 145 \quad \text{(50-cent coins remaining)}.
     \]

   - Sasa also spent $ \frac{5}{7} $ of her 20-cent coins:
     \[
     \frac{5}{7} \times \frac{7}{8}x = \frac{5}{8}x \quad \text{(20-cent coins spent)}.
     \]
   - The number of 20-cent coins left:
     \[
     \frac{7}{8}x - \frac{5}{8}x = \frac{2}{8}x = \frac{1}{4}x.
     \]

3. **Coins Left:**
   - Total coins left:
     \[
     \frac{1}{8}x - 145 + \frac{1}{4}x.
     \]
   - Simplifying the expression $ \frac{1}{4}x $ to have the same denominator:
     \[
     \frac{2}{8}x = \frac{1}{4}x.
     \]
   - Combine the terms:
     \[
     \frac{1}{8}x - 145 + \frac{2}{8}x = \frac{3}{8}x - 145.
     \]
   - According to the problem statement, this amount is equal to $ \frac{2}{7}x $:
     \[
     \frac{3}{8}x - 145 = \frac{2}{7}x.
     \]

4. **Solve for $ x $:**
   - Multiply every term by $ 56 $ to clear the fractions:
     \[
     56 \times \left( \frac{3}{8}x - 145 \right) = 56 \times \frac{2}{7}x,
     \]
     \[
     7 \times 3x - 56 \times 145 = 16x,
     \]
     \[
     21x - 8120 = 16x.
     \]
   - Move terms involving $ x $ to one side:
     \[
     21x - 16x = 8120,
     \]
     \[
     5x = 8120,
     \]
     \[
     x = \frac{8120}{5} = 1624.
     \]

5. **Calculate Coins Left:**
   - Substitute $ x = 1624 $:
     - Number of 20-cent coins left:
       \[
       \frac{1}{4} \times 1624 = 406.
       \]
     - Number of 50-cent coins left:
       \[
       \frac{1}{8} \times 1624 - 145 = 203 - 145 = 58.
       \]

6. **Calculate the Total Money Left:**
   - Total value of 20-cent coins:
     \[
     406 \times 0.20 = 81.20 \quad \text{(dollars)}.
     \]
   - Total value of 50-cent coins:
     \[
     58 \times 0.50 = 29.00 \quad \text{(dollars)}.
     \]
   - Total amount of money left:
     \[
     81.20 + 29.00 = 110.20.
     \]

So, the total amount of money Sasa had left is **$110.20**.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How would the result change if Sasa spent a different fraction of her coins?
2. What if the value of the 50-cent coins spent was different?
3. How many coins did Sasa start with initially for each denomination?
4. What is the total value of the coins before any were spent?
5. How would the problem change if the number of coins left was different?

**Tip:** When dealing with fractions of a total, ensure you express all parts of the problem in a consistent manner to avoid mistakes.

Solve the problem of determining the total amount of money Sasa had left after spending 145 fifty-cent coins and 5/7 of her twenty-cent coins. This problem covers concepts of algebra, fractions, and money calculations. Suitable for students in Grades 6-8.

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