Soft Drinks Orange
Two 24-packs for $20; one 24-pack for $15
Root Beer
One 24-pack for $18
Cream Soda
One 12-pack for $10
A consumer needs to purchase at least 60 soft drinks for a picnic.
Which of the following combinations is the most cost-effective?
A.
2 packs of Orange and 1 pack of Cream Soda
B.
3 one 24-pack of Orange
C.
2 packs of Root Beer and 1 pack of Cream Soda
D.
5 packs of cream Soda
To determine the most cost-effective combination for purchasing at least 60 soft drinks, we need to calculate the cost per drink for each type and then find the total cost for each combination.
Cost Per Drink:
- Orange:
- Two 24-packs for $20: 2048=0.4167\frac{20}{48} = 0.41674820=0.4167 dollars per drink
- One 24-pack for $15: 1524=0.625\frac{15}{24} = 0.6252415=0.625 dollars per drink
- Root Beer:
- One 24-pack for $18: 1824=0.75\frac{18}{24} = 0.752418=0.75 dollars per drink
- Cream Soda:
- One 12-pack for $10: 1012=0.8333\frac{10}{12} = 0.83331210=0.8333 dollars per drink
Cost Analysis for Each Combination:
A. 2 packs of Orange and 1 pack of Cream Soda
- 2 packs of Orange (using the more cost-effective deal): 2048×48=40\frac{20}{48} \times 48 = 404820×48=40 drinks
- 1 pack of Cream Soda: 121212 drinks
- Total drinks: 40+12=5240 + 12 = 5240+12=52 drinks (which does not meet the requirement)
B. 3 packs of Orange
- Buying 3 packs at $15 each (not the best deal): 3×15=453 \times 15 = 453×15=45 drinks
- Total cost: 454545 drinks at 1524×45=28.125\frac{15}{24} \times 45 = 28.1252415×45=28.125 dollars per drink
- Total cost: 45 drinks×0.625=28.12545 \text{ drinks} \times 0.625 = 28.12545 drinks×0.625=28.125 dollars (Note: Only 45 drinks)
C. 2 packs of Root Beer and 1 pack of Cream Soda
- 2 packs of Root Beer (24-pack each): 2×18=362 \times 18 = 362×18=36 drinks
- 1 pack of Cream Soda: 121212 drinks
- Total drinks: 36+12=4836 + 12 = 4836+12=48 drinks (which does not meet the requirement)
D. 5 packs of Cream Soda
- 5 packs of Cream Soda: 5×12=605 \times 12 = 605×12=60 drinks
- Total cost: 5×10=505 \times 10 = 505×10=50 dollars
Conclusion:
Since the only option that meets the requirement of at least 60 drinks is option D, and it costs $50 for 60 drinks, it is the most cost-effective option given the constraints.
Correct Answer: D. 5 packs of Cream Soda