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 to find the total amount of money Sasa had left.

### Step 1: Define variables
Let:
- $ x $ be the total number of coins Sasa initially had.
- $ \frac{7}{8}x $ is the number of 20-cent coins.
- $ \frac{1}{8}x $ is the number of 50-cent coins.

### Step 2: Information about how much Sasa spent

Sasa spent:
- 145 of her 50-cent coins. Since $ 1/8 $ of her total coins are 50-cent coins, the number of remaining 50-cent coins is:
  \[
  \frac{1}{8}x - 145
  \]
- $ \frac{5}{7} $ of her 20-cent coins. The number of remaining 20-cent coins is:
  \[
  \frac{2}{7} \times \frac{7}{8}x = \frac{2}{8}x = \frac{1}{4}x
  \]

### Step 3: Total number of remaining coins
Sasa had $ \frac{2}{7}x $ coins left after spending. These remaining coins consist of both 20-cent and 50-cent coins. Thus:
\[
\frac{1}{4}x + \left( \frac{1}{8}x - 145 \right) = \frac{2}{7}x
\]
Now, solve for $ x $.

### Step 4: Solve for $ x $
Combine terms:
\[
\frac{1}{4}x + \frac{1}{8}x - 145 = \frac{2}{7}x
\]
To simplify, find a common denominator for $ \frac{1}{4}x $ and $ \frac{1}{8}x $. The least common denominator is 8:
\[
\frac{1}{4}x = \frac{2}{8}x
\]
Thus, the equation becomes:
\[
\frac{2}{8}x + \frac{1}{8}x - 145 = \frac{2}{7}x
\]
\[
\frac{3}{8}x - 145 = \frac{2}{7}x
\]

### Step 5: Eliminate the fractions
Multiply the entire equation by 56 (the least common denominator of 8 and 7) to eliminate the fractions:
\[
56 \times \left( \frac{3}{8}x - 145 \right) = 56 \times \frac{2}{7}x
\]
This simplifies to:
\[
21x - 8120 = 16x
\]

### Step 6: Solve for $ x $
Now, isolate $ x $:
\[
21x - 16x = 8120
\]
\[
5x = 8120
\]
\[
x = \frac{8120}{5} = 1624
\]

### Step 7: Calculate the number of coins left
Now that we know $ x = 1624 $, the total number of coins left is:
\[
\frac{2}{7} \times 1624 = 464
\]

### Step 8: Calculate the number of 20-cent and 50-cent coins left
- The number of 20-cent coins left is $ \frac{1}{4} \times 1624 = 406 $.
- The number of 50-cent coins left is $ \frac{1}{8} \times 1624 - 145 = 203 - 145 = 58 $.

### Step 9: Calculate the total amount of money left
The total value of the remaining coins is:
\[
406 \times 0.20 + 58 \times 0.50 = 81.20 + 29 = 110.20
\]

Thus, Sasa has **$110.20** left.

Would you like any further details or explanations? Here are some related questions you might explore:

1. How many 50-cent coins did Sasa initially have?
2. How many 20-cent coins did Sasa spend?
3. What is the total number of coins Sasa spent?
4. If Sasa spent a different amount of 50-cent coins, how would that affect the final answer?
5. How can we adjust this solution if different fractions of coins were spent?

**Tip**: When solving word problems, always double-check how variables are used and ensure they correspond to the right quantities!

Learn how to solve a word problem involving fractions and currency. Sasa starts with a total number of 20-cent and 50-cent coins, spends $72.50 worth of 50-cent coins and 5/7 of the 20-cent coins, and is left with 2/7 of her coins. The problem requires solving for the total amount of money she has left. Suitable for Grades 8-10.

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