Free Practice Question
PS · Problem Solving
605-655
Fractions/Ratios/Decimals
Two containers of equal capacity are filled with a blend of oil and water. In the first container, the oil to water ratio is 4:9, while in the second container, it is 5:15. When both containers are combined into a larger one, what will be the resulting ratio of oil to water?
Answer Choices
Correct answer marked belowA
4:15
B
1:4
C
17:35
D
19:36
29:75
Correct
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Official Explanation
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We have two containers with equal capacity. Each container has a mixture of oil and water, but with different ratios.
First Container: Oil to water ratio is 4:9.
Second Container: Oil to water ratio is 5:15.
We need to combine both containers into a larger one and find the new oil to water ratio in the combined mixture.
Step 1: Assign a Common Capacity to Both Containers
Since both containers have equal capacity, let's assume each container has a total volume that makes the ratios easy to work with. A good approach is to choose a number that is a common multiple of the denominators in the ratios to avoid fractions.
First container ratio: 4:9 (total parts = 4 + 9 = 13)
Second container ratio: 5:15 (which simplifies to 1:3, total parts = 1 + 3 = 4)
The least common multiple (LCM) of 13 and 4 is 52. So, let's assume each container has a total volume of 52 units. This way, the amounts of oil and water in each container will be whole numbers.
Step 2: Calculate Oil and Water in the First Container
First container ratio: Oil:Water = 4:9
Total parts = 4 (oil) + 9 (water) = 13 parts
Volume of oil in first container = (4 / 13) * 52 = 4 * 4 = 16 units
Volume of water in first container = (9 / 13) * 52 = 9 * 4 = 36 units
So, first container: 16 oil + 36 water = 52 total
Step 3: Calculate Oil and Water in the Second Container
Second container ratio: Oil:Water = 5:15, which simplifies to 1:3
Total parts = 1 (oil) + 3 (water) = 4 parts
Volume of oil in second container = (1 / 4) * 52 = 13 units
Volume of water in second container = (3 / 4) * 52 = 39 units
So, second container: 13 oil + 39 water = 52 total…
First Container: Oil to water ratio is 4:9.
Second Container: Oil to water ratio is 5:15.
We need to combine both containers into a larger one and find the new oil to water ratio in the combined mixture.
Step 1: Assign a Common Capacity to Both Containers
Since both containers have equal capacity, let's assume each container has a total volume that makes the ratios easy to work with. A good approach is to choose a number that is a common multiple of the denominators in the ratios to avoid fractions.
First container ratio: 4:9 (total parts = 4 + 9 = 13)
Second container ratio: 5:15 (which simplifies to 1:3, total parts = 1 + 3 = 4)
The least common multiple (LCM) of 13 and 4 is 52. So, let's assume each container has a total volume of 52 units. This way, the amounts of oil and water in each container will be whole numbers.
Step 2: Calculate Oil and Water in the First Container
First container ratio: Oil:Water = 4:9
Total parts = 4 (oil) + 9 (water) = 13 parts
Volume of oil in first container = (4 / 13) * 52 = 4 * 4 = 16 units
Volume of water in first container = (9 / 13) * 52 = 9 * 4 = 36 units
So, first container: 16 oil + 36 water = 52 total
Step 3: Calculate Oil and Water in the Second Container
Second container ratio: Oil:Water = 5:15, which simplifies to 1:3
Total parts = 1 (oil) + 3 (water) = 4 parts
Volume of oil in second container = (1 / 4) * 52 = 13 units
Volume of water in second container = (3 / 4) * 52 = 39 units
So, second container: 13 oil + 39 water = 52 total…
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I
IMar 25, 2024
thank you for sharing
S
SujoyAug 28, 2024
thank you very much!
What this question tests
What it tests
Your ability to convert between fractions, ratios, and decimals and to reason proportionally.
Common trap
Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.
Details
Difficulty
605-655
Type
PS
Category