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Ratio and Proportion Mixture Problem: Calculate Morning Delight Volume from Juice A Amount
Mathematics
Grade 7 (Junior High School)
Question Content
Two blended fruit juices are made from mixing pure juices in the following ratios: Morning Delight: 3:1:5 for juices A, B and C respectively; Tropical Surprise: 2:3:3 for juices A, B and C respectively. 120 litres of juice A is used to make Tropical Surprise. How many litres of Morning Delight could the same amount of juice A make?
Correct Answer
160
Detailed Solution Steps
1
Step 1: Analyze the ratio for Tropical Surprise. The ratio of juice A to the total volume of Tropical Surprise is 2:(2+3+3) = 2:8 = 1:4.
2
Step 2: Calculate the total volume of Tropical Surprise made with 120L of juice A. Since 1 part of A makes 4 parts of total juice, total Tropical Surprise volume = 120 × 4 = 480L. This confirms the proportion of A in Tropical Surprise is 120/480 = 1/4, matching the ratio.
3
Step 3: Analyze the ratio for Morning Delight. The ratio of juice A to the total volume of Morning Delight is 3:(3+1+5) = 3:9 = 1:3. This means 1 part of A makes 3 parts of total Morning Delight.
4
Step 4: Calculate the total volume of Morning Delight that can be made with 120L of juice A. Using the 1:3 proportion, total Morning Delight volume = 120 × 3 = 160L.
Knowledge Points Involved
1
Ratio and Proportion
Ratios compare quantities of different components in a mixture, while proportions show the relationship between a part and the whole. In mixture problems, ratios are used to find the fraction of each component relative to the total mixture volume, then scaled to actual quantities.
2
Scaling Ratios to Actual Quantities
When given the actual amount of one component in a ratio, you first find the fraction of that component in the total mixture, then use multiplication to find the total volume of the mixture, or vice versa. This is done by dividing the actual component amount by its ratio share, then multiplying by the total ratio sum.
3
Mixture Problem Solving
For problems involving mixed substances, you use component ratios to relate individual ingredient amounts to the total mixture volume. This requires first simplifying the ratio to find the fractional share of each ingredient, then applying that to known quantities to solve for unknown volumes.
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