To solve this problem, let's break it down step by step.

Step 1: Define the variables

Let:

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

Step 2: Sasa's expenditures

Sasa spent:

• 145 50-cent coins (as given in the problem).
• $\frac{5}{7}$ of the 20-cent coins.

Step 3: Set up the equation for the 50-cent coins

Initially, the number of 50-cent coins was $\frac{1}{8}x$. After spending 145 50-cent coins, the remaining number of 50-cent coins is: $\frac{1}{8}x - 145$

Step 4: Set up the equation for the 20-cent coins

Initially, Sasa had $\frac{7}{8}x$ 20-cent coins. After spending $\frac{5}{7}$ of them, she had $\frac{2}{7}$ of her 20-cent coins left. So 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 5: Remaining coins

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

Step 6: Solve for $x$

Now, solve the equation $\frac{1}{4}x + \frac{1}{8}x - 145 = \frac{2}{7}x$.

1. Find a common denominator for the fractions: $\frac{1}{4}x = \frac{2}{8}x$ So the equation becomes: $\frac{2}{8}x + \frac{1}{8}x - 145 = \frac{2}{7}x$ $\frac{3}{8}x - 145 = \frac{2}{7}x$

2. Eliminate the fractions by multiplying the entire equation by 56 (the least common denominator of 8 and 7): $56 \times \left(\frac{3}{8}x\right) - 56 \times 145 = 56 \times \left(\frac{2}{7}x\right)$ $21x - 8120 = 16x$

3. Rearrange to isolate $x$: $21x - 16x = 8120$ $5x = 8120$ $x = \frac{8120}{5} = 1624$

So, the total number of coins $x$ is 1624.

Step 7: Calculate how much money Sasa has left

Now, calculate the remaining amount of money:

1. The remaining number of 20-cent coins is $\frac{1}{4}x = \frac{1}{4} \times 1624 = 406$.

   • The value of the remaining 20-cent coins is $406 \times 0.20 = 81.20$ dollars.

2. The remaining number of 50-cent coins is $\frac{1}{8}x - 145 = \frac{1}{8} \times 1624 - 145 = 203 - 145 = 58$.

   • The value of the remaining 50-cent coins is $58 \times 0.50 = 29$ dollars.

Step 8: Total amount of money Sasa has left

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

Thus, Sasa has $110.20 left.

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Would you like to explore further details on any specific step? Here are some related questions:

1. How to solve equations with multiple fractions?
2. How are fractions simplified in linear equations?
3. How to calculate the total number of coins from fractions of a total?
4. How to handle multiple variables in coin-related word problems?
5. What is the importance of setting up correct relationships in word problems?

Tip: Always define all variables clearly when solving a word problem—it helps to set up equations systematically.