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 go through this step-by-step to find the total amount of money Sasa has left.

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

### 2. Spending details:
- Sasa spent 145 50-cent coins, which is equivalent to $ 145 \times 0.50 = 72.50 $ dollars.
- She also spent $ \frac{5}{7} $ of her 20-cent coins.

Now, Sasa is left with $ \frac{2}{7}x $ coins in total.

### 3. Equation setup for remaining coins:
We know the total number of coins after spending is $ \frac{2}{7}x $. This means:

\[
\text{Remaining coins} = \frac{2}{7}x
\]

This total consists of:
- $ \frac{2}{7} \times \frac{7}{8}x = \frac{2}{8}x = \frac{1}{4}x $ 20-cent coins (since she spent $ \frac{5}{7} $ of them).
- The remaining number of 50-cent coins after spending 145 of them would be:
\[
\frac{1}{8}x - 145
\]

So, the total number of coins left is:
\[
\frac{1}{4}x + \left( \frac{1}{8}x - 145 \right) = \frac{2}{7}x
\]

### 4. Solve for $ x $:
Let’s set up the equation to solve for $ x $.

\[
\frac{1}{4}x + \left( \frac{1}{8}x - 145 \right) = \frac{2}{7}x
\]

To eliminate fractions, multiply the entire equation by 56 (the least common denominator of 4, 8, and 7):

\[
56 \times \left( \frac{1}{4}x \right) + 56 \times \left( \frac{1}{8}x - 145 \right) = 56 \times \left( \frac{2}{7}x \right)
\]

This simplifies to:

\[
14x + 7x - 8120 = 16x
\]

Combine like terms:

\[
21x - 8120 = 16x
\]

Move all terms involving $ x $ to one side:

\[
21x - 16x = 8120
\]

\[
5x = 8120
\]

Solve for $ x $:

\[
x = \frac{8120}{5} = 1624
\]

### 5. Find the total money left:
Now that we know $ x = 1624 $, let's calculate the number of coins left and the total amount of money Sasa has.

- **Remaining 20-cent coins**: 
\[
\frac{1}{4} \times 1624 = 406 \, \text{20-cent coins}.
\]
The value of these coins is:
\[
406 \times 0.20 = 81.20 \, \text{dollars}.
\]

- **Remaining 50-cent coins**: 
\[
\frac{1}{8} \times 1624 - 145 = 203 - 145 = 58 \, \text{50-cent coins}.
\]
The value of these coins is:
\[
58 \times 0.50 = 29 \, \text{dollars}.
\]

### 6. Total amount of money left:
The total amount of money Sasa has left is:
\[
81.20 + 29 = 110.20 \, \text{dollars}.
\]

### Final Answer:
Sasa has **$110.20** left.

---

Would you like any more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the solution change if Sasa spent a different fraction of her 20-cent coins?
2. What if Sasa spent $ \frac{3}{4} $ of her 50-cent coins instead of 145 coins?
3. How would you calculate the remaining amount if she spent an unknown number of coins?
4. Can you verify this solution by recalculating the total coins after each transaction?
5. What if Sasa had another denomination of coins, say 10-cent coins?

**Tip**: When dealing with fractions and word problems, breaking the problem into small steps helps ensure clarity and accuracy!

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.

Learn how to solve a coin problem where Sasa spends fractions of her 20-cent and 50-cent coins. This step-by-step solution involves algebraic equations and fractional coin amounts, suitable for students in Grades 8-10.

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