Let $x$ be the total number of coins Sasa originally had.

Step 1: Determine the number of 20-cent and 50-cent 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: Account for the coins spent.

• Sasa spent 145 of her 50-cent coins, leaving $\frac{1}{8}x - 145$ 50-cent coins.
• Sasa also spent $\frac{5}{7}$ of her 20-cent coins, leaving $\frac{2}{7} \times \frac{7}{8}x = \frac{1}{4}x$ 20-cent coins.

After spending these coins, the total number of coins left is given as $\frac{2}{7}x$. So, the remaining coins consist of some 20-cent coins and some 50-cent coins:

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

Step 3: Set up the equation and solve for $x$.

Simplify the left-hand side:

$\frac{1}{4}x + \frac{1}{8}x - 145 = \frac{2}{7}x$

Find a common denominator for $\frac{1}{4}x$ and $\frac{1}{8}x$:

$\frac{2}{8}x + \frac{1}{8}x = \frac{3}{8}x$

Thus, the equation becomes:

$\frac{3}{8}x - 145 = \frac{2}{7}x$

Step 4: Solve for $x$.

Multiply both sides of the equation by 56 (the least common denominator of 8 and 7):

$56 \times \left( \frac{3}{8}x - 145 \right) = 56 \times \frac{2}{7}x$

This simplifies to:

$21x - 8120 = 16x$

Now, subtract $16x$ from both sides:

$5x = 8120$

Finally, divide by 5:

$x = 1624$

Step 5: Calculate the remaining money.

• The total number of 20-cent coins Sasa had originally is $\frac{7}{8} \times 1624 = 1421$ 20-cent coins.
• The total number of 50-cent coins Sasa had originally is $\frac{1}{8} \times 1624 = 203$ 50-cent coins.

After spending 145 50-cent coins, Sasa had $203 - 145 = 58$ 50-cent coins left.

After spending $\frac{5}{7}$ of her 20-cent coins, she had $\frac{2}{7} \times 1421 = 406$ 20-cent coins left.

The total amount of money left is:

$406 \times 0.20 + 58 \times 0.50 = 81.20 + 29 = 110.20$

Final Answer:

Sasa had $110.20 left.

Would you like a detailed explanation on any specific step? Here are some related questions:

1. How do you find fractional parts of a number in general?
2. Why is multiplying by the least common denominator helpful in solving equations with fractions?
3. What would happen if Sasa had more or fewer 50-cent coins?
4. How do you check that the solution satisfies all the conditions?
5. How do you solve similar problems with three or more types of coins?

Tip: When dealing with coins or percentages, always track how fractions of the total change after each transaction.