Text Task (Word Problems) "Bananas are 10% more expensive than oranges, and apples are 20% cheaper than bananas."

[politexnik]

Bananas are 10% more expensive than oranges, and apples are 20% cheaper than bananas.

1. By what percentage is a banana more expensive than an apple? (Answer: 25%)

2. What percentage is the amount paid for 3 kg of bananas more than the amount paid for 2 kg of oranges? (Answer: 65%)

3. How many kg of bananas can be bought for the amount paid for 20 kg of apples and 22 kg of oranges? (Answer: 36kg)

4. By what percent is an apple cheaper than an orange? (Answer: 12%)

I need all 4 solutions.

 

[stapel]

Bananas are 10% more expensive than oranges, and apples are 20% cheaper than bananas.

1. By what percentage is a banana more expensive than an apple? (Answer: 25%)

2. What percentage is the amount paid for 3 kg of bananas more than the amount paid for 2 kg of oranges? (Answer: 65%)

3. How many kg of bananas can be bought for the amount paid for 20 kg of apples and 22 kg of oranges? (Answer: 36kg)

4. By what percent is an apple cheaper than an orange? (Answer: 12%)

I need all 4 solutions.

You've been given the four answers. Are you saying that you're having difficulty in arriving at those answers?

If so, then please reply with a clear listing of your thoughts and efforts so far, so that we can begin to work with you.

Thank you!

 

[Dr.Peterson]

Bananas are 10% more expensive than oranges, and apples are 20% cheaper than bananas.

1. By what percentage is a banana more expensive than an apple? (Answer: 25%)

2. What percentage is the amount paid for 3 kg of bananas more than the amount paid for 2 kg of oranges? (Answer: 65%)

3. How many kg of bananas can be bought for the amount paid for 20 kg of apples and 22 kg of oranges? (Answer: 36kg)

4. By what percent is an apple cheaper than an orange? (Answer: 12%)

I need all 4 solutions.

There are several ways you could approach these, depending on what you have learned. That is one reason we need to see your attempts, or at least to be told what you know that might be relevant. I wouldn't want to give you a method of solution that you don't understand at all.

If you know algebra, you could define variables x, y, and z representing the prices of a banana, an orange, and an apple, and write some equations.

But you could also just restate what you are told. If a banana costs 10% more than an orange, then what could you multiply the price of an orange by to find the price of a banana? And so on..

 

[Dr.Peterson]

Bananas are 10% more expensive than oranges, and apples are 20% cheaper than bananas.

1. By what percentage is a banana more expensive than an apple? (Answer: 25%)

2. What percentage is the amount paid for 3 kg of bananas more than the amount paid for 2 kg of oranges? (Answer: 65%)

3. How many kg of bananas can be bought for the amount paid for 20 kg of apples and 22 kg of oranges? (Answer: 36kg)

4. By what percent is an apple cheaper than an orange? (Answer: 12%)

I need all 4 solutions.

I will now try to restate these problems for clarity, as I did in the other thread:

Bananas are 10% more expensive than oranges, and apples are 20% cheaper than bananas.

B is 10% greater than O, and A is 20% less than B.​

1. By what percentage is a banana more expensive than an apple? (Answer: 25%)

By what percent is B greater than A? (I get 25%.)​

2. What percentage is the amount paid for 3 kg of bananas more than the amount paid for 2 kg of oranges? (Answer: 65%)

By what percent is 3 B greater than 2 O? (I get 65%.)​

3. How many kg of bananas can be bought for the amount paid for 20 kg of apples and 22 kg of oranges? (Answer: 36kg)

What multiple of B is equal to 20 A + 22 O? (I get 36.)​

4. By what percent is an apple cheaper than an orange? (Answer: 12%)

By what percent is A less than O? (I get 12%.)​

I was wrong; these are not as awkward as the problem in the other thread; I have no doubt about their interpretation.

 

[The Highlander]

I was wrong; these are not as awkward as the problem in the other thread; I have no doubt about their interpretation.

Indeed, I had no difficulty interpreting these and coming up with the given answers either.
The approach I adopted was to set the cost of an orange to £1 ⇒ bananas cost £1.11 and apples 88p each; everything else then flowed from that without a hitch.

Except that, as I pointed out in the other thread, Parts 2 & 3 can only be done if the (very unlikely) assumption is made that every banana and every orange and every apple all have exactly the same mass!

Of course, it would be possible to assume, instead, that the percentages given referred to the relationships between the per kg price of each fruit (again, this was not stated or implied anywhere) but if that was the case then Parts 1 & 4 are no longer possible to calculate (unless you make the same outlandish assumption that every fruit weighs the same!).

Another reason to suspect that this OP doesn't provide full details in his/her posts. ?

 

[Dr.Peterson]

Another reason to suspect that this OP doesn't provide full details in his/her posts.

... or, as I expect, that the problems themselves are written to require such simplifying assumptions, which is common in exercises that are aimed at unsophisticated students who are not being taught about real-life mathematics. I think it's more likely the teacher's/author's fault, from my experience with elementary textbook problems, than the student's.

I myself would say that in problems 1 and 4 you have to assume that the pricing is per item, while in problems 2 and 3, the pricing must be per kilogram. Either is a reasonable interpretation of the given data, but not both, and the problem ideally would have made all that explicit.

I have to admit that as I ponder this, I am only gradually realizing just how bad a problem this is, and that it must be the author who would have made it so bad. No incomplete reporting by the student could make a good problem so inconsistent.

 

[The Highlander]

... or, as I expect, that the problems themselves are written to require such simplifying assumptions, which is common in exercises that are aimed at unsophisticated students who are not being taught about real-life mathematics. I think it's more likely the teacher's/author's fault, from my experience with elementary textbook problems, than the student's.

I have to admit that as I ponder this, I am only gradually realizing just how bad a problem this is, and that it must be the author who would have made it so bad. No incomplete reporting by the student could make a good problem so inconsistent.

Usted es demasiado amable! ?