https://file.aiquickdraw.com/mathbot/file/1730380034815yrdpfmgm.jpg

Let’s solve this step-by-step.

Let:
- $ x $ = the total amount of money Jeff initially received from his mother.
- $ d $ = the amount of money Jeff used each day.

### Step 1: Set Up the Equations

1. **After 7 days:** Jeff has used $ 7d $ amount of money. We know that at the end of the 7th day, he was left with $\frac{1}{4}$ of his initial amount. Therefore:
   \[
   x - 7d = \frac{1}{4}x
   \]

2. **After 9 days:** Jeff has used $ 9d $ amount of money. At this point, he has $10 left. So:
   \[
   x - 9d = 10
   \]

### Step 2: Solve the Equations

From the first equation:
\[
x - 7d = \frac{1}{4}x
\]
Rearrange it to solve for $ d $:
\[
x - \frac{1}{4}x = 7d
\]
\[
\frac{3}{4}x = 7d
\]
\[
d = \frac{3}{28}x
\]

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

Jeff received **$280** from his mother.

Would you like more details on the solution? 

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Here are some related questions for practice:

1. If Jeff had $15 left at the end of the 9th day, how much did he initially receive?
2. How much money would Jeff have if he used only half the daily amount after 7 days?
3. If Jeff spent $5 more each day, how much would he have on the 10th day?
4. How much would Jeff need to have at the beginning if he wanted $20 left on the 10th day?
5. How many days could Jeff sustain spending if he wanted to have $50 remaining?

**Tip:** When given percentages or fractions of an unknown value in word problems, set up variables to represent unknowns and build equations based on given conditions.

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?

Solve a word problem involving linear equations to determine how much Jeff initially received from his mother, given that he spends an equal amount daily. After 7 days, he has 1/4 of his starting amount left, and after 9 days, he has $10 remaining. This algebraic problem is suitable for Grades 7-9.

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