Let's define the problem and solve it step by step:

Step 1: Define Variables

• Let $x$ be the total number of coins.
• The number of 20-cent coins is $\frac{7}{8}x$.
• The number of 50-cent coins is $\frac{1}{8}x$.

Step 2: Coins Left After Spending

• Sasa spent 145 of her 50-cent coins, so the remaining number of 50-cent coins is: $\frac{1}{8}x - 145$
• Sasa also spent $\frac{5}{7}$ of her 20-cent coins. So the remaining 20-cent coins are: $\frac{7}{8}x - \frac{5}{7} \times \frac{7}{8}x = \frac{2}{7} \times \frac{7}{8}x = \frac{2}{8}x = \frac{1}{4}x$

Step 3: Total Coins Left

According to the problem, after spending, Sasa had $\frac{2}{7}x$ coins left. So the sum of the remaining 20-cent and 50-cent coins is: $\frac{1}{4}x + \left( \frac{1}{8}x - 145 \right) = \frac{2}{7}x$

Step 4: Solve for $x$

Now, we solve the equation: $\frac{1}{4}x + \frac{1}{8}x - 145 = \frac{2}{7}x$ First, find a common denominator for $\frac{1}{4}x$ and $\frac{1}{8}x$: $\frac{1}{4}x = \frac{2}{8}x$ So the equation becomes: $\frac{2}{8}x + \frac{1}{8}x - 145 = \frac{2}{7}x$ Simplify the left side: $\frac{3}{8}x - 145 = \frac{2}{7}x$ Now, eliminate the fractions by multiplying through by 56 (the least common multiple of 8 and 7): $56 \times \left( \frac{3}{8}x - 145 \right) = 56 \times \frac{2}{7}x$ This gives: $21x - 8120 = 16x$ Simplify: $21x - 16x = 8120$ $5x = 8120$ $x = 1624$

Step 5: Find the Total Amount of Money Left

Now that we know $x = 1624$, we can find how many coins are left:

• The number of remaining 20-cent coins is: $\frac{1}{4} \times 1624 = 406$
• The number of remaining 50-cent coins is: $\frac{1}{8} \times 1624 - 145 = 203 - 145 = 58$

The total amount of money Sasa has left is:

• From 20-cent coins: $406 \times 0.20 = 81.20$ dollars.
• From 50-cent coins: $58 \times 0.50 = 29$ dollars.

Thus, the total amount of money Sasa has left is: $81.20 + 29 = 110.20 \text{ dollars}$

Final Answer:

Sasa has $\boxed{110.20}$ dollars left.

Would you like further clarification or a deeper breakdown of any step?

Here are 5 related questions to explore:

1. What is the importance of solving equations with fractions in this type of problem?
2. How do you determine the number of remaining coins after spending a fraction of them?
3. How would the solution change if the total amount spent had been different?
4. What strategies can be used to simplify equations involving fractions?
5. How do you check the consistency of your results in problems involving multiple variables?

Tip: When solving equations with fractions, finding a common denominator early on can simplify the process significantly.