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The ratio of the ages of five members of the Kauffman family is 1 to 2
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12 Nov 2021, 06:46
12 Nov 2021, 06:46
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The ratio of the ages of five members of the Kauffman family is 1 to 2 to 3 to 4 to 6. If one of them is 12 years old, which of the following could be the age of the eldest of the five?
A. 18
B. 48
C. 60
D. 84
E. 96
A. 18
B. 48
C. 60
D. 84
E. 96
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Re: The ratio of the ages of five members of the Kauffman family is 1 to 2
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12 Nov 2021, 08:00
12 Nov 2021, 08:00
1
Carcass wrote:
The ratio of the ages of five members of the Kauffman family is 1 to 2 to 3 to 4 to 6. If one of them is 12 years old, which of the following could be the age of the eldest of the five?
A. 18
B. 48
C. 60
D. 84
E. 96
A. 18
B. 48
C. 60
D. 84
E. 96
Given: The ratio of the 5 ages = 1 : 2 : 3 : 4 : 6
So, for example, the five ages could be 1, 2, 3, 4, and 6
Or if we multiply all parts of the original ratio by 2, the five ages could also be 2, 4, 6, 8, and 12. In this case, the eldest child is 12 years old.
Or if we multiply all parts of the original ratio by 3, the five ages could also be 3, 6, 9, 12, and 18. In this case, the eldest child is 18 years old (and one of the other children is 12 years old).
Answer: A
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Re: The ratio of the ages of five members of the Kauffman family is 1 to 2
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12 Nov 2021, 10:38
12 Nov 2021, 10:38
1
Start by writing the ages with a scaling factor of x:
1x:2x:3x:4x:6x
Let's start at the 1x. If we substitute the 12 for the 1x, this implies that x is 12. This would make 6x = 72, which is not an option.
Let's try the other side. If we make 6x = 12, then x = 2 and the oldest is 12. This is not an option, either, but given that these ages are closer together, it is probably a good idea to try 4x next.
With 4x = 12, we have x = 3 and the oldest is 18. This is answer A.
Given that we have found an answer, we are safe to stop here. If you want to test the others to be sure (not recommended), you'll find that 3x = 12 makes the oldest 24 and 2x = 12 makes the oldest 36.
1x:2x:3x:4x:6x
Let's start at the 1x. If we substitute the 12 for the 1x, this implies that x is 12. This would make 6x = 72, which is not an option.
Let's try the other side. If we make 6x = 12, then x = 2 and the oldest is 12. This is not an option, either, but given that these ages are closer together, it is probably a good idea to try 4x next.
With 4x = 12, we have x = 3 and the oldest is 18. This is answer A.
Given that we have found an answer, we are safe to stop here. If you want to test the others to be sure (not recommended), you'll find that 3x = 12 makes the oldest 24 and 2x = 12 makes the oldest 36.
