Fruit Punch Concentrate Decision
Ms. LeBlanc's Grade 7 class is running a drink stand at the spring fair. They must make 24 L of fruit punch and have two concentrate options. Recipe A mixes concentrate and water in a 3:5 ratio; concentrate costs $4.20 per 1.5 L bottle. Recipe B is 40% concentrate by volume; concentrate costs $5.60 per 2 L bottle. Store rules require buying whole bottles, and leftover concentrate cannot be returned. The class wants the lowest cost per litre of finished punch, but the teacher also wants the punch to be at least 37% concentrate so the flavour is strong enough. Water is free.
1. For each recipe, determine the litres of concentrate needed for 24 L of punch, the number of bottles that must be purchased, and the total concentrate cost. Then compute the cost per litre of finished punch.
Read the worked answer
Recipe A: the ratio 3:5 has 8 parts total, so concentrate is 3/8 of the punch. Concentrate = 24 × 3/8 = 9 L. Bottles = 9 ÷ 1.5 = 6 exactly. Cost = 6 × $4.20 = $25.20. Cost per litre = 25.20 ÷ 24 = $1.05.
Recipe B: concentrate = 40% of 24 = 0.40 × 24 = 9.6 L. Bottles = 9.6 ÷ 2 = 4.8, so 5 whole bottles must be bought. Cost = 5 × $5.60 = $28.00. Cost per litre = 28.00 ÷ 24 ≈ $1.1667, about $1.17. Buying 5 bottles gives 10 L, so 0.4 L is left over.
2. Which recipe satisfies the teacher's 'at least 37% concentrate' rule? Which should the class choose? Justify with both strength and cost, including any leftover issue.
Read the worked answer
Recipe A is 9 L concentrate out of 24 L total = 9/24 = 37.5%, so it meets the rule. Recipe B is 40%, so it also meets the rule. A is cheaper: $25.20 versus $28.00, a saving of $2.80. A also uses exactly 6 bottles with no leftover, while B leaves 0.4 L that cannot be returned. Choose Recipe A unless the class specifically wants the slightly stronger 40% punch and is willing to pay more and waste concentrate.
3. The supplier offers Recipe B concentrate at $4.60 per 2 L bottle. Recalculate Recipe B's cost and decide whether the recommendation changes.
Read the worked answer
Recipe B still needs 9.6 L of concentrate, so it still requires 5 bottles. New cost = 5 × $4.60 = $23.00. Cost per litre = 23.00 ÷ 24 ≈ $0.958, about $0.96. This is now cheaper than Recipe A at $1.05 per litre. The recommendation changes to Recipe B if the class accepts 40% strength and the 0.4 L leftover. The comparison must be redone whenever a price changes.