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A shop sells two brands of orange juice, Brand A and Brand B, as shown - Junior Cycle Mathematics - Question b - 2016
Question b
A shop sells two brands of orange juice, Brand A and Brand B, as shown. (i) Find which brand, A or B, is cheaper per litre. Show all of your working out. Samantha ... show full transcript
Worked Solution & Example Answer:A shop sells two brands of orange juice, Brand A and Brand B, as shown - Junior Cycle Mathematics - Question b - 2016
Step 1
(i) Find which brand, A or B, is cheaper per litre.
Answer
To determine the cost per litre for both brands, we need to convert the price based on the given volumes.
Brand A:
- Price: €3.60 for 2 litres.
- Cost per litre = €3.60 / 2 litres = €1.80 per litre.
Brand B:
- Price: €1.50 for 750 ml (which is 0.75 litres).
- Cost per litre = €1.50 / 0.75 litres = €2.00 per litre.
Comparison:
- Brand A: €1.80 per litre
- Brand B: €2.00 per litre
Therefore, Brand A is cheaper.
Step 2
(ii) Find the lowest price that she could pay to do this, by buying Brand A, Brand B, or a combination of both.
Answer
To buy at least 5 litres of orange juice at the lowest cost, we can calculate multiple combinations.
-
Buying only Brand A:
- Cost for 5 litres = 5 x €3.60 / 2 = 5 x €1.80 = €9.00.
-
Buying only Brand B:
- Number of 750 ml bottles needed = 5 litres / 0.75 litres = 6.67 (which rounds up to 7 bottles).
- Cost for 7 bottles = 7 x €1.50 = €10.50.
-
Combination of both brands:
- For example, buying 3 bottles of Brand A and 2 bottles of Brand B:
- Cost = 3 x €1.80 + 2 x €2.00 = €5.40 + €4.00 = €9.40.
After evaluating all combinations, the lowest price option remains with purchasing only Brand A for €9.00.