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In a tropical drink, the ratio of pineapple juice to mango juice to orange juice is 15 : 9 : 4 - HSC - SSCE Mathematics Standard - Question 23 - 2020 - Paper 1
Question 23
In a tropical drink, the ratio of pineapple juice to mango juice to orange juice is 15 : 9 : 4. (a) How much orange juice is needed if the tropical drink is to cont... show full transcript
Worked Solution & Example Answer:In a tropical drink, the ratio of pineapple juice to mango juice to orange juice is 15 : 9 : 4 - HSC - SSCE Mathematics Standard - Question 23 - 2020 - Paper 1
Step 1
How much orange juice is needed if the tropical drink is to contain 3 litres of pineapple juice?
Answer
The ratio of pineapple juice to orange juice is 15 : 4.
To find out how much orange juice is needed, we can set up a proportion.
Letting parts of pineapple juice be represented as 15, we have:
1 part of pineapple juice = ( \frac{3 \text{ L}}{15} )
Therefore, for orange juice:
[ 4 \text{ parts of orange juice} = 4 \times \frac{3}{15} = \frac{12}{15} = 0.8 \text{ L} \text{ or } 800 \text{ mL} \text{ of orange juice required.} ]
Step 2
To completely fill the container with the tropical drink, how many litres of mango juice are required?
Answer
The dimensions of the container are:
- Length = 40 cm
- Width = 20 cm
- Height = 35 cm
To find the capacity of the container:
[ \text{Capacity} = 40 \times 20 \times 35 = 28,000 \text{ cm}^3 = 28 \text{ L} ]
The total number of parts in the ratio is: [ 15 + 9 + 4 = 28 ]
Now, finding the amount of mango juice required: [ \text{Amount of mango juice required} = \frac{9}{28} \times 28 \text{ L} = 9 \text{ L} ]