Alice loves rope licorice. She is offered the three following deals: Deal 1: She can buy licorice ropes at a rate of
1.92 per foot. Deal 3: She can buy licorice ropes for $0.14 per inch. Alice wants to buy 1.5 yards of licorice rope at the lowest price. What deal should she select? (Note: 1 yard = 3 feet; 1 foot = 12 inches) A. Deal 1 B. Deal 2 C. Deal 3 D. Deal 1 and 3 provide equal prices for the licorice
The Correct Answer and Explanation is:
To determine which deal Alice should select, let’s break down the cost for each option.
Convert yards to feet and inches
- 1 yard = 3 feet.
- Alice wants to buy 1.5 yards of licorice rope. 1.5 yards×3 feet/yard=4.5 feet1.5 \, \text{yards} \times 3 \, \text{feet/yard} = 4.5 \, \text{feet}1.5yards×3feet/yard=4.5feet
Deal 1: Price per foot
- The price for licorice rope in Deal 1 is $1.92 per foot.
- Since Alice wants 4.5 feet, the total cost for Deal 1 is: 1.92 per foot×4.5 feet=8.641.92 \, \text{per foot} \times 4.5 \, \text{feet} = 8.641.92per foot×4.5feet=8.64
Deal 2: Price per inch
- The price for licorice rope in Deal 3 is $0.14 per inch.
- Since 1 foot = 12 inches, Alice wants 4.5 feet of rope, which is: 4.5 feet×12 inches/foot=54 inches4.5 \, \text{feet} \times 12 \, \text{inches/foot} = 54 \, \text{inches}4.5feet×12inches/foot=54inches
- The total cost for Deal 3 is: 0.14 per inch×54 inches=7.560.14 \, \text{per inch} \times 54 \, \text{inches} = 7.560.14per inch×54inches=7.56
Comparison
- Deal 1 costs $8.64 for 4.5 feet of licorice.
- Deal 3 costs $7.56 for 4.5 feet of licorice.
Conclusion
Alice should select Deal 3, which offers the lowest price of $7.56 for 4.5 feet of licorice rope. The correct answer is C. Deal 3.
