We are given the following information about Sasa's coins:

1. Let $x$ be the total number of coins.
2. $\frac{7}{8}x$ are 20-cent coins.
3. $\frac{1}{8}x$ are 50-cent coins.
4. After spending 145 50-cent coins and $\frac{5}{7}$ of the 20-cent coins, she had $\frac{2}{7}x$ coins left.

We are tasked with finding the total amount of money Sasa has left.

Step 1: Calculate the number of 50-cent coins Sasa initially had.

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

Step 2: Calculate the number of 20-cent coins Sasa initially had.

The total number of 20-cent coins is $\frac{7}{8}x$. After spending $\frac{5}{7}$ of these, the number of remaining 20-cent coins is: $\frac{7}{8}x - \frac{5}{7} \times \frac{7}{8}x = \frac{7}{8}x - \frac{5}{8}x = \frac{2}{8}x = \frac{1}{4}x$

Step 3: Set up the equation for the total number of remaining coins.

After spending some of the coins, Sasa is left with $\frac{2}{7}x$ coins. This includes the remaining 50-cent and 20-cent coins. Therefore, the equation is: $\left( \frac{1}{8}x - 145 \right) + \frac{1}{4}x = \frac{2}{7}x$

Step 4: Solve the equation.

First, express $\frac{1}{4}x$ as $\frac{2}{8}x$, so that all terms have a denominator of 8: $\frac{1}{8}x - 145 + \frac{2}{8}x = \frac{2}{7}x$ Combine the terms on the left-hand side: $\frac{3}{8}x - 145 = \frac{2}{7}x$ Now, subtract $\frac{2}{7}x$ from both sides: $\frac{3}{8}x - \frac{2}{7}x = 145$ To combine these terms, we need a common denominator. The least common denominator of 8 and 7 is 56. Rewriting the fractions: $\frac{3}{8}x = \frac{21}{56}x, \quad \frac{2}{7}x = \frac{16}{56}x$ Thus, the equation becomes: $\frac{21}{56}x - \frac{16}{56}x = 145$ $\frac{5}{56}x = 145$ Solve for $x$: $x = 145 \times \frac{56}{5} = 1624$

Step 5: Calculate the total amount of money Sasa has left.

Now that we know $x = 1624$, we can find how many 50-cent and 20-cent coins Sasa has left.

• The number of remaining 50-cent coins is: $\frac{1}{8} \times 1624 - 145 = 203 - 145 = 58$ The value of the remaining 50-cent coins is: $58 \times 0.50 = 29 \text{ dollars}$

• The number of remaining 20-cent coins is: $\frac{1}{4} \times 1624 = 406$ The value of the remaining 20-cent coins is: $406 \times 0.20 = 81.20 \text{ dollars}$

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

Final Answer:

Sasa has $110.20 left.

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Do you need further details or have any questions?

Related Questions:

1. What would be the result if Sasa had spent half of her 50-cent coins instead of 145?
2. If Sasa had 10 more 20-cent coins initially, what would her remaining total be?
3. How would the result change if Sasa spent $90 worth of 50-cent coins?
4. What if Sasa had only $\frac{1}{8}x$ coins left instead of $\frac{2}{7}x$?
5. How can the same problem be solved using a different method, such as substitution?

Tip:

Always check your work by verifying the total number of remaining coins matches what's expected.