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Clever | Portal My Classes | McGraw Hill C9, L1: A Growing Economy UpStudy Thoth AI Rates \& proportional relations khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-graphing-prop-rel/e/comparing-proportional-r... Explore Search Khan Academy Donate 14440 Hey, let's keep the momentum! On to week 3 of your streak! 2 week streak Level 7 (i) \( \square \) \( 2 / 7 \) skills 8th grade COURSE: 8TH GRADE > UNIT 3 Lesson 1: Graphing proportional relationships Rates \& proportional relationships Attempted •86\% Graphing proportional relationship... Graphing proportional relationship... Andrei loves to bake, and plum tarts are his specialty. Plums are on sale for \( \$ 3.25 \) for 2 pounds at the farmer's market. At the supermarket, plums are being sold according to the following equation, where \( P \) is price in dollars and \( L \) is pounds: \[ P=1.75 L \] Where do plums cost less, at the farmer's market or the supermarket? Choose 1 answer: (A) The farmer's market B The supermarket (C) Plums cost the same amount at the farmer's market and the supermarket.
Ask by Macdonald Norton. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Plums are cheaper at the farmer's market.
Solution
To determine where plums cost less, let's compare the price per pound at both the farmer's market and the supermarket.
**Farmer's Market:**
- **Total Cost:** \$3.25 for 2 pounds
- **Price per Pound:** \$3.25 ÷ 2 = **\$1.625 per pound**
**Supermarket:**
- **Price Equation:** \( P = 1.75L \)
- **Price per Pound:** \$1.75 per pound
**Comparison:**
- **Farmer's Market:** \$1.625 per pound
- **Supermarket:** \$1.75 per pound
Since **\$1.625** (farmer's market) is **less than** \$1.75 (supermarket), plums are cheaper at the **farmer's market**.
### **Answer:**
**(A) The farmer's market**
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Simplify this solution Bonus Knowledge
To determine where plums cost less, let's first find the cost of plums per pound at both locations. At the farmer's market, the price is \( \$3.25 \) for 2 pounds, which means it costs \( \$1.625 \) per pound. Meanwhile, the supermarket sells plums for \( P=1.75L \), meaning it costs \( \$1.75 \) per pound. Thus, at the farmer’s market, plums are cheaper! Now for a quick tip: when comparing rates, always convert prices to a consistent unit—such as price per pound in this case. A common mistake is comparing total prices without considering the quantity, which can easily mislead your decision!
