https://file.aiquickdraw.com/mathbot/file/17265113532477blo4ybj.jpg

The problem in the image is asking for an inequality and solution based on the following scenario:

---

**Problem:**

Lilly’s dog weighs 90 pounds. A healthy weight for her dog would be less than 75 pounds. If Ashley’s dog can lose an average of 1.25 pounds per week with a new diet and additional walks, how long would it take until her dog reaches a healthy weight?

---

Let's break it down:

### Step 1: Define a variable
Let \( x \) represent the number of weeks it will take for the dog to reach a healthy weight.

### Step 2: Write the inequality
The dog's weight decreases by 1.25 pounds each week. Starting at 90 pounds, the dog's weight after \( x \) weeks will be \( 90 - 1.25x \). We want the weight to be less than 75 pounds, so the inequality is:

\[
90 - 1.25x < 75
\]

### Step 3: Solve the inequality
To solve for \( x \):

1. Subtract 90 from both sides:

\[
-1.25x < 75 - 90
\]
\[
-1.25x < -15
\]

2. Divide both sides by -1.25, and since we're dividing by a negative number, we reverse the inequality:

\[
x > \frac{-15}{-1.25}
\]
\[
x > 12
\]

So, it will take more than 12 weeks for the dog to reach a weight below 75 pounds.

### Step 4: Interpretation
In real life, this means that it will take more than 12 weeks (or approximately 13 weeks) of following the new diet and exercise plan for Lilly’s dog to reach a healthy weight.

---

Would you like more details, or do you have any questions?

### 5 Related Questions:
1. What would the inequality look like if the dog started at 100 pounds?
2. How would the solution change if the dog lost 2 pounds per week instead?
3. What if the target weight was 70 pounds instead of 75 pounds?
4. How would the equation change if the dog's weight increased instead of decreased?
5. What would happen if the dog plateaued after losing weight for a certain number of weeks?

### Tip:
When solving inequalities, always remember to flip the inequality sign when multiplying or dividing by a negative number.

Lilly's dog weighs 90 pounds. A healthy weight for her dog would be less than 75 pounds. If Ashley's dog can lose an average of 1.25 pounds per week with a new diet and additional walks, how long would it take until her dog reaches a healthy weight?

Solve an inequality to determine how many weeks it will take for Lilly's dog, weighing 90 pounds, to reach a healthy weight below 75 pounds, losing 1.25 pounds per week. Suitable for Grades 6-8, this problem teaches core concepts of inequalities and linear equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation