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.

We are given that Sasa had some 20-cent and 50-cent coins. The total number of coins is $ x $, and they are divided as follows:
- $ \frac{7}{8}x $ are 20-cent coins.
- $ \frac{1}{8}x $ are 50-cent coins.

### Step 1: Determine the initial number of coins
The number of 50-cent coins is $ \frac{1}{8}x $. After spending \$72.50 worth of 50-cent coins, we know Sasa spent 145 50-cent coins, so:

\[
\frac{1}{8}x = 145
\]

Multiplying both sides by 8:

\[
x = 145 \times 8 = 1160
\]

Thus, the total number of coins $ x $ is 1160.

### Step 2: Determine the initial number of 20-cent and 50-cent coins
- The number of 20-cent coins is $ \frac{7}{8} \times 1160 = 1015 $.
- The number of 50-cent coins is $ \frac{1}{8} \times 1160 = 145 $, which matches the information given.

### Step 3: Spending 50-cent and 20-cent coins
- Sasa spent all 145 of the 50-cent coins.
- Sasa spent $ \frac{5}{7} $ of the 20-cent coins, so the number of 20-cent coins she spent is:

\[
\frac{5}{7} \times 1015 = 725 \text{ (20-cent coins spent)}.
\]

Thus, the number of 20-cent coins remaining is:

\[
1015 - 725 = 290.
\]

### Step 4: Calculate the number of remaining coins
After spending the coins, Sasa had $ \frac{2}{7}x $ coins left. Since $ x = 1160 $, the number of remaining coins is:

\[
\frac{2}{7} \times 1160 = 331.43 \approx 331 \text{ coins (rounded)}.
\]

### Step 5: Calculate the total amount of money left
Sasa has 290 remaining 20-cent coins and 0 50-cent coins left (since she spent all of them). The total value of the remaining 20-cent coins is:

\[
290 \times 0.20 = 58 \text{ dollars}.
\]

Thus, Sasa has \$58 left.

### Final Answer:
Sasa has $ \mathbf{58} $ dollars left.

Do you want more details or have any questions?

Here are 5 related questions for practice:
1. If Sasa had 50 more 20-cent coins, what would the total value of her remaining coins be?
2. How many coins would Sasa have left if she spent 3/7 of her total number of coins instead?
3. If Sasa spent half of her remaining 20-cent coins, how much money would she have left?
4. How many 50-cent coins would Sasa need to spend if she had to use \$50 worth of them?
5. What would be the total value of coins if Sasa had double the number of 50-cent coins initially?

**Tip**: Always verify the relationship between proportions and total values when dealing with problems involving fractions of total quantities.

Learn how to solve a coin problem involving 20-cent and 50-cent coins with fractions and proportional calculations. This example demonstrates how to find the total number of coins and money left after spending some coins. Suitable for students in Grades 6-8.

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