Fatima plans to spend at least $15 and at most $20 on sketch pads and pencils. If she buys 2 sketch pads, how many pencils can she buy while staying in her price range? sketch pads cost $3.25 each and pencils cost $0.75 each, whats the inequality?

To solve this problem, we need to set up an inequality based on Fatima's spending limits. Here's the step-by-step breakdown:

### 1. Define Variables:
- Let $ x $ represent the number of pencils Fatima buys.
- The cost of each sketch pad is $3.25.
- The cost of each pencil is $0.75.

### 2. Write the Total Cost Expression:
Fatima buys 2 sketch pads, so the cost for the sketch pads is:
\[
2 \times 3.25 = 6.50 \text{ dollars}
\]

If she buys $ x $ pencils, the cost for the pencils will be:
\[
0.75x \text{ dollars}
\]

Therefore, the total cost is:
\[
6.50 + 0.75x \text{ dollars}
\]

### 3. Set Up the Inequality:
Fatima wants to spend between $15 and $20. Therefore, the total cost should satisfy the inequality:
\[
15 \leq 6.50 + 0.75x \leq 20
\]

### 4. Solve the Inequality:
#### a. Solve the left side:
\[
15 \leq 6.50 + 0.75x
\]
Subtract 6.50 from both sides:
\[
8.50 \leq 0.75x
\]
Now, divide both sides by 0.75:
\[
x \geq \frac{8.50}{0.75} = 11.33
\]
Since $ x $ must be a whole number (you can't buy a fraction of a pencil), round 11.33 up to 12. So, $ x \geq 12 $.

#### b. Solve the right side:
\[
6.50 + 0.75x \leq 20
\]
Subtract 6.50 from both sides:
\[
0.75x \leq 13.50
\]
Now, divide both sides by 0.75:
\[
x \leq \frac{13.50}{0.75} = 18
\]

### 5. Combine the Results:
The inequality for the number of pencils Fatima can buy is:
\[
12 \leq x \leq 18
\]

Thus, Fatima can buy between **12 and 18 pencils** while staying within her price range of $15 to $20.

Would you like further details on this solution, or do you have any questions?

### Related Questions:
1. How would the inequality change if the price of pencils was $1.00 each?
2. What if Fatima buys only 1 sketch pad? How many pencils could she buy within the price range?
3. How many total items (sketch pads and pencils) could Fatima purchase if she spent exactly $20?
4. What if Fatima wants to buy exactly 15 pencils? How much would she spend?
5. If Fatima buys 2 sketch pads and 14 pencils, what will her total expenditure be?

### Tip:
When solving inequalities with decimals, be careful with rounding—always consider whether to round up or down based on the context of the problem.

Learn how to solve the inequality problem for Fatima, who plans to spend between $15 and $20 on sketch pads and pencils. This detailed solution covers setting up the inequality, calculating costs for pencils and sketch pads, and determining the range of pencils Fatima can buy within her budget.

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