Question
9:19 AM Tue Feb 4 25\% learnx-svc.k12.com Back ! Lesson 8.1-Mid-Year Test, Part 1 Caleb Menu SEMESTER TEST Mid-Year Test Part 1 More Read Focus James buys \( 2 \frac{4}{5} \) kilograms of red potatoes. He buys yellow potatoes that weigh \( \frac{3}{4} \) as much as the red potatoes. How many kilograms of yellow potatoes does James buy? Enter your answer as a mixed number in simplest form by filling in the boxes. \( \square \) \( \square \) kg 15 16 17 18 19 20 21 22 23 24
Ask by Daniel Pena. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
James buys \( 2 \frac{1}{10} \) kilograms of yellow potatoes.
Solution
To determine how many kilograms of yellow potatoes James buys, follow these steps:
1. **Convert the Mixed Number to an Improper Fraction:**
James buys \( 2 \frac{4}{5} \) kilograms of red potatoes.
\[
2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5} \text{ kg}
\]
2. **Calculate \( \frac{3}{4} \) of the Red Potatoes:**
He buys yellow potatoes that weigh \( \frac{3}{4} \) as much as the red potatoes.
\[
\frac{3}{4} \times \frac{14}{5} = \frac{3 \times 14}{4 \times 5} = \frac{42}{20}
\]
3. **Simplify the Fraction:**
\[
\frac{42}{20} = \frac{21}{10} = 2 \frac{1}{10} \text{ kg}
\]
**Final Answer:**
James buys \( 2 \frac{1}{10} \) kilograms of yellow potatoes.
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Simplify this solution Beyond the Answer
To find out how many kilograms of yellow potatoes James buys, we start with the weight of the red potatoes: \( 2 \frac{4}{5} \) kilograms. First, convert the mixed number into an improper fraction. \( 2 \frac{4}{5} = \frac{14}{5} \). Next, since the yellow potatoes weigh \( \frac{3}{4} \) as much as the red potatoes, we calculate \( \frac{3}{4} \) of \( \frac{14}{5} \): \[ \text{Weight of yellow potatoes} = \frac{3}{4} \times \frac{14}{5} = \frac{3 \times 14}{4 \times 5} = \frac{42}{20} = \frac{21}{10} = 2 \frac{1}{10}. \] So, James buys \( 2 \frac{1}{10} \) kilograms of yellow potatoes. Now, you just need to fill in the boxes: \( 2 \) and \( \frac{1}{10} \) kg!
