Unit 6
5 marks · Normal1. A recipe for fruit squash mixes orange juice and water in the ratio 3:7. You have 540 ml of squash prepared.
Work out how much orange juice is in the squash.
Suppose each ml of orange juice costs $0.02, and the amount of orange juice is directly proportional to the total cost. Find the total cost of all the orange juice in the squash.
Describe, using set-builder notation, the set O of all possible volumes (in ml) of orange juice you could have if the squash was made in this ratio but with a total volume up to 1000 ml.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 162 ml
(b) $3.24 $
(c) O = {x | x = 3k, 0 < k < 334}
Common mistakes: Confusing parts of ratio; Using the wrong multiplier; Not using set notation
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Find correct fraction of orange juice or identify calculation method.
A1 (a) · 1 mark · Correct answer for orange juice (162 ml). (follow-through)
M2 (b) · 1 mark · Multiply orange juice volume by $0.02. (follow-through)
A2 (b) · 1 mark · Correct cost ($3.24). (follow-through)
B1 (c) · 1 mark · Set is fully and correctly described using set-builder notation.
Worked solution
a) Total parts = 3 + 7 = 10. Orange juice = (3/10) × 540 = 162 ml.
b) Orange juice: 162 ml. Cost per ml = $0.02. Total cost: 162 × 0.02 = $3.24.
c) Let k be the number of batches of 10 ml (must be a positive whole number): O = {x | x = 3k, 0 < k < 334} (since 10k ≤ 1000 → k < 100).