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 $ x $ be the total number of coins Sasa had initially.

### Step 1: Determine the number of each type of coin.
- The number of 20-cent coins is $ \frac{7}{8}x $.
- The number of 50-cent coins is $ \frac{1}{8}x $.

### Step 2: Analyze the situation after Sasa spent some of her coins.
- Sasa spent 145 50-cent coins. Therefore, the total number of 50-cent coins she initially had must have been at least 145. This implies:
  \[
  \frac{1}{8}x \geq 145.
  \]
  Multiplying both sides by 8:
  \[
  x \geq 1160.
  \]
  
- Sasa also spent $ \frac{5}{7} $ of her 20-cent coins. The number of 20-cent coins remaining is $ \frac{2}{7} $ of $ \frac{7}{8}x $, which is:
  \[
  \frac{2}{7} \times \frac{7}{8}x = \frac{2}{8}x = \frac{1}{4}x.
  \]

### Step 3: Total coins left.
Sasa was left with $ \frac{2}{7}x $ coins in total, so the sum of the remaining 20-cent and 50-cent coins should equal $ \frac{2}{7}x $. The number of remaining 20-cent coins is $ \frac{1}{4}x $, so the number of remaining 50-cent coins is:
\[
\frac{2}{7}x - \frac{1}{4}x.
\]
To simplify this, find a common denominator:
\[
\frac{2}{7}x = \frac{8}{28}x \quad \text{and} \quad \frac{1}{4}x = \frac{7}{28}x,
\]
so:
\[
\frac{8}{28}x - \frac{7}{28}x = \frac{1}{28}x.
\]
Thus, the number of remaining 50-cent coins is $ \frac{1}{28}x $.

### Step 4: Calculate the total value of the remaining coins.
The total value of the remaining 20-cent coins is:
\[
\frac{1}{4}x \times 0.20 = 0.05x.
\]
The total value of the remaining 50-cent coins is:
\[
\frac{1}{28}x \times 0.50 = \frac{0.50}{28}x = 0.017857x.
\]

Thus, the total value of the remaining coins is:
\[
0.05x + 0.017857x = 0.067857x.
\]

### Step 5: Solve for $ x $.
Since Sasa spent 145 50-cent coins, the total number of 50-cent coins initially was $ \frac{1}{8}x = 145 $, so:
\[
x = 145 \times 8 = 1160.
\]

### Step 6: Calculate the total amount of money Sasa has left.
Now substitute $ x = 1160 $ into the expression for the total value of the remaining coins:
\[
0.067857 \times 1160 = 78.71.
\]

Thus, the total amount of money Sasa has left is **$78.71**.

---

Would you like more details, or do you have any further questions? Here are 5 related questions you can explore:

1. How would the answer change if Sasa spent $ \frac{6}{7} $ of her 20-cent coins?
2. What if Sasa had spent 160 50-cent coins instead of 145?
3. Can you determine how much money Sasa initially had before spending any coins?
4. How would the problem change if Sasa had 9/10 of her coins as 20-cent coins instead of 7/8?
5. How can this be solved using algebraic expressions for both types of coins?

**Tip:** Always break down a problem step by step, especially when dealing with fractions and large numbers.

Solve the problem where Sasa has a mix of 20-cent and 50-cent coins, spends a portion, and calculates the remaining amount of money. The solution involves algebraic manipulation and proportion calculations, suitable for Grades 8-10.

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