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Consider the question: the ratio of Joe's mass to his father is `3/7` ; what is Joe's...

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durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted July 29, 2013 at 12:53 PM via web

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Consider the question: the ratio of Joe's mass to his father is `3/7` ; what is Joe's mass if his father weighs 88kg?

I find the question to be ambiguous and it has been interpreted in two different ways, rendering two different answers: 37.7 kg or 66 kg. Which one is correct? Could they both be correct? Please state your reasons. 

I favor the first answer, believing that Joe's weight is `3/7`  of his father's but my colleagues favor the second stating that it is `3/7:4/7`

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted July 29, 2013 at 1:13 PM (Answer #1)

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If the ratio represents Joe's mass to his father, then 37 would be 37:1, meaning Joe's mass is 37 times his father's.  If his father weighs 88 kg, then Joe would weigh 88 * 37 = 3256 kg.  This answer doesn't make sense.  If Joe's weight was 37 of his father's, then the problem should be stated as "the ratio of the father's mass to Joe's mass is 37".  Then the answer would be 88 * 1/37 = 2.4 kg.  This answer doesn't make sense either unless Joe is a newborn.

If the problem is supposed to read 3:7 instead of 37, then it makes a lot more sense.  If the ratio of Joe to his father is 3:7, then...

3:7 = x:88
7x = 264
x = 37.7

Joe's weight would be 37.7 kg.  I think this is how the problem is meant to be interpretted.

Top Answer

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 29, 2013 at 1:41 PM (Answer #2)

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The confusion lies in the use of  `3/7` to represent a ratio. We are so used to seeing `3/7` as a fraction that it is hard to think of it in another way.

The ratio of the weights is 3 to 7; also written 3:7 or `3/7` .

So `"son'sweight"/"father'sweight"=3/7` or the ratio of the son's weight to the father's weight is 3 to 7.(son's weight:father's weight=3:7)

`x/88=3/7 ==> x=(88*3)/7=264/7~~37.7"kg"`

Note that if Joe weighs 66kg then the ratio of his weight to his father's weight is `66/88=3/4` or 3:4.

**To confuse matters further we also use this notation when talking about odds (versus probability.) If the odds in favor are 3:4 then the probability in favor is 3/7. Here 3:4 is a ratio of winners to losers, as opposed to probability winners to total. **

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