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.

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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.