12. KNitting Nastia knitted two scarves for her dolls. One was $$ 8 \frac{3}{4} $$ inches long. The other was $$ 1 \frac{1}{2} $$ inches shorter than the first. How long was the second scarf?

Question

UpStudy AI · Accepted Answer

To determine the length of the second scarf knitted by Nastia, let's break down the problem step by step.

### Given:
1. **First Scarf Length:** $$ 8 \frac{3}{4} $$ inches
2. **Difference in Length:** $$ 1 \frac{1}{2} $$ inches shorter than the first scarf

### Objective:
Find the length of the **second scarf**.

### Step 1: Convert Mixed Numbers to Improper Fractions or Decimals

It's often easier to work with decimals or improper fractions when performing arithmetic operations.

- **First Scarf:**
  $$
  8 \frac{3}{4} = 8 + \frac{3}{4} = 8 + 0.75 = 8.75 \text{ inches}
  $$

- **Difference:**
  $$
  1 \frac{1}{2} = 1 + \frac{1}{2} = 1 + 0.5 = 1.5 \text{ inches}
  $$

### Step 2: Subtract the Difference from the First Scarf's Length

To find the second scarf's length, subtract the difference from the first scarf's length.

$$
\text{Second Scarf Length} = \text{First Scarf Length} - \text{Difference}
$$

$$
\text{Second Scarf Length} = 8.75 \text{ inches} - 1.5 \text{ inches} = 7.25 \text{ inches}
$$

### Step 3: Convert Back to a Mixed Number (Optional)

If you prefer the answer as a mixed number:

$$
7.25 \text{ inches} = 7 \frac{0.25}{1} = 7 \frac{1}{4} \text{ inches}
$$

### **Answer:**
The second scarf was **7 ¼ inches** long.
The second scarf was 7 ¼ inches long.

KNitting Nastia knitted two scarves for her dolls. One was inches
long. The other was inches shorter than the first. How long was the
second scarf?

Upstudy AI Solution

Answer

Solution

Given:

Objective:

Step 1: Convert Mixed Numbers to Improper Fractions or Decimals

Step 2: Subtract the Difference from the First Scarf’s Length

Step 3: Convert Back to a Mixed Number (Optional)

Answer:

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KNitting Nastia knitted two scarves for her dolls. One was inches long. The other was inches shorter than the first. How long was the second scarf?