Need input on a ratio word problem: 6 jumping jacks for every 3 push-ups

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Exeat

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Hello All-

My daughter's math teacher gave the class a problem the answer to which has caused some controversy. The problem is as follows:

Susan knows she eats too much during the holidays so she is trying to work out more to maintain her weight and health. She began her training doing 6 jumping jacks for every 3 push-ups, but them she injured her ankle. After her injury, Susan completed 4 jumping jacks for every 5 push-ups. During a training session, after her injury, Susan completed 20 push-ups. How many jumping jacks was Susan completing before her injury?

The teacher's answer is: Susan was completing 24 jumping jacks before her injury (4 x 6 = 24). I don't see the logic in that answer. Does anyone have any insight into this?

Thanks.
 
Susan was doing 6 jumping jacks for every 3 push-ups, that means 2 jumping jacks for every 1 push-up, so for 20 push-ups it was 40 jumping jacks.
This is my solution, but maybe I did not understand correctly...
 
skaa said:
Susan was doing 6 jumping jacks for every 3 push-ups, that means 2 jumping jacks for every 1 push-up, so for 20 push-ups it was 40 jumping jacks.
This is my solution, but maybe I did not understand correctly...
Click to expand...

That is the same answer I got, but the teacher is firm that the answer is 24.
 
Denis said:
Simplified problem a bit;
most teachers are long-winded: often creates confusion!
24 is correct.
HINT:
6 : 3 - 24 : 12 (before)
4 : 5 - 16 : 20 (after)
Click to expand...
No No No! I feel that you are reading too much into this problem. Where does it say that she does the same number of sets after her injury as before? This problem can not be done! It simply is another case of a teacher......
As always, it's just an imagination of your figment
 
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So does anyone else concur with Jomo that the problem cannot be done? I would like to approach the teacher about this problem, but I want to have a decent degree of confidence in what I say.

I appreciate your input.
 
Exeat said:
So does anyone else concur with Jomo that the problem cannot be done? I would like to approach the teacher about this problem, but I want to have a decent degree of confidence in what I say.

I appreciate your input.
Click to expand...
I need to be clear. The way it was worded I truly believe I am correct. Having said that you need to think what was meant to be said. I did not read your title talking about ratios. If this is in the ratio section then if you read into the question that you were to keep the same ratio then the answer is surely 24.
 
I sort of agree with Jomo. If we read the problem literally, then it could be any answer it feels like (aka unsolvable) because there's no information about how many sets Susan did before her injury. If we make some assumptions to account for unstated information, I can think of two possible solutions to this problem, one of which is the answer given by your teacher and the other your initial answer.

If we assume that Susan did the same number of push-ups both before and after her injury, such that the number of jumping jacks is the only variable, we arrive at your initial answer of 40. Alternatively, if we assume that the number of sets of push-ups and jumping jacks is the same both before and after her injury, we get a different answer. Post-injury, Susan did 20 push-ups, which is 4 sets. In her pre-injury workout, 4 sets means she did 12 push-ups and 24 jumping jacks.

If I were grading this problem, I would give credit for either answer. I would also give partial credit for any other answer, as long as the student gives justification for how they came up with that answer. Because, it really is a poorly written problem, relying on the student to make an assumption about what happened, which should never happen.
 
ksdhart2 said:
I sort of agree with Jomo. If we read the problem literally, then it could be any answer it feels like (aka unsolvable) because there's no information about how many sets Susan did before her injury. If we make some assumptions to account for unstated information, I can think of two possible solutions to this problem, one of which is the answer given by your teacher and the other your initial answer.

If we assume that Susan did the same number of push-ups both before and after her injury, such that the number of jumping jacks is the only variable, we arrive at your initial answer of 40. Alternatively, if we assume that the number of sets of push-ups and jumping jacks is the same both before and after her injury, we get a different answer. Post-injury, Susan did 20 push-ups, which is 4 sets. In her pre-injury workout, 4 sets means she did 12 push-ups and 24 jumping jacks.

If I were grading this problem, I would give credit for either answer. I would also give partial credit for any other answer, as long as the student gives justification for how they came up with that answer. Because, it really is a poorly written problem, relying on the student to make an assumption about what happened, which should never happen.
Click to expand...
I agree that you get 40 JJ if you keep the same 2 to 1 pre injury ratio. However, this person did NOT keep this ratio post injury. They tell us that the ratio post injury was 4 JJ to 5 PU which is NOT 2 to 1. So how can 40 be the answer IF we assume this is a ratio problem (and it really is a ratio problem if there is going to be any answer)?
 
There simply isn't enough information. We are asked how many jumping jacks Susan did before her injury so any information about what she did after her injury is irrelevant. We are told that, before her injury, Susan did "6 jumping jacks for every 3 push-ups" but we are not told how many push ups she did before her injury.
 
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