https://file.aiquickdraw.com/mathbot/file/17303791294671pdy0ye8.jpg

Let’s analyze the problem step-by-step.

Let:
- $ x $ be the total amount of money Jeff initially received.
- $ d $ be the daily amount he spent.

### Step 1: Information given
1. At the end of the 7th day, he had $ \frac{1}{4} $ of his initial amount $ x $ left.
   \[
   x - 7d = \frac{1}{4}x
   \]

2. At the end of the 9th day, he had $10 left.
   \[
   x - 9d = 10
   \]

### Step 2: Set up equations
From the above information, we have two equations:

1. $ x - 7d = \frac{1}{4}x $
2. $ x - 9d = 10 $

### Step 3: Solve Equation 1 for $ d $
Rearrange Equation 1 to express $ d $ in terms of $ x $:

1. $ x - 7d = \frac{1}{4}x $
   \[
   7d = x - \frac{1}{4}x
   \]
   \[
   7d = \frac{3}{4}x
   \]
   \[
   d = \frac{3}{28}x
   \]

### Step 4: Substitute $ d $ in Equation 2
Now, substitute $ d = \frac{3}{28}x $ into the second equation:

\[
x - 9\left(\frac{3}{28}x\right) = 10
\]
\[
x - \frac{27}{28}x = 10
\]
\[
\frac{1}{28}x = 10
\]
\[
x = 10 \times 28
\]
\[
x = 280
\]

### Conclusion
The initial amount Jeff received from his mother was **$280**.

Would you like more details on any specific part? 

Here are some related questions to further explore:
1. How much did Jeff spend each day?
2. How much money did Jeff have left after each day?
3. What would change if he spent a different amount daily?
4. How would the answer change if he was left with a different fraction on day 7?
5. Could this approach be used for different types of spending patterns?

**Tip:** When setting up equations, double-check the units and context to ensure accuracy.

Jeff's mother gave him some money. He used an equal amount of money each day. At the end of the 7th day, he was left with 1/4 of how much he had at first. At the end of the 9th day, he was left with $10. How much did Jeff receive from his mother?

Learn how to solve an algebra problem involving fractions and linear equations. Jeff's mother gave him some money, and he spent an equal amount each day. By the end of the 7th and 9th days, specific amounts were left. Find out the total amount given with a step-by-step solution suitable for Grades 8-10.

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