Word Problem Help!!! Fruits order from Highest to Lowest by cost?!?
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Start naming the variables. If I were to do this problem, I would assume,
Price of 1 apple = A, Price of 1 banana = B, Price of 1 Orange = O & Price of 1 pear = P. Next I will consider the statements:
Apples are 3 times more expensive than oranges → A > O ....... and continue
Please show us what you have tried and exactly where you are stuck.
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Please share your work/thoughts about this problem.
Otis
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Sure thing! Where are you stuck?
This exercise is typical for beginning algebra students who have just been taught how to (1) translate English statements about equality into algebraic equations and (2) solve simple equations, using substitution when necessary. If those things seem unfamiliar, please let us know.
My approach uses part of what lev888 mentioned and also part of what Subhotosh did. Instead of relating each of the four fruits to something else, I would relate three of them to the remaining one. Because the given information already relates apples & oranges and also relates bananas & oranges, I would try to relate pears & oranges. That way, three of the fruit prices (apple, banana, pear) can each be expressed in terms of the fourth price (orange), and those expressions will make the ordering obvious.
A method for doing it begins by translating given English statements to algebraic statements. I would use Subhotosh's symbols, but I would write equations instead of inequalities.
Do you know how to write the exercise's first three sentences as equations, using variable symbols A,B,P,O?
Please show us how far you can get. If you see anything that you don't understand, ask us! If you have not studied algebra, then please tell us where you saw this exercise and why you're interested in it. Thanks.
lev888
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By something else I meant something other than monetary value.
Sorry I thought I posted my notes here they are! I think it’s apples pears banana oranges
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Otis
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Hi. I agree that the price of one orange is smallest. Your work shows A>O, but how did you determine that A is also greater than both B and P? My result is different.
Is your class currently studying inequalities? I found it easier to use the given equalities, instead, to express prices A,B,P in terms of price O because we may see the answer directly from those expressions.
Dr.Peterson
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Does anyone else have a problem with the wording of this?
First, many people consider "3 times more expensive" to be different from "3 times as expensive". I don't, because I recognize it as an idiom, but it's at least debatable.
Second, "a third as cheap" is even more unclear. Many people (possibly including me) would say it means "3 times as expensive", taking "cheap" as the reciprocal of "expensive". (Would you say "twice as cheap" to mean "twice as expensive"? I wouldn't. So why would this mean 1/3 as expensive? Yet this feels too pedantic.)
Since this problem is at least partly about interpreting English, they should use standard (unambiguous) English!
0----O----+----A
We can't yet place B or P, so we can move on to O and B. Where does B go?
In any case, none of these are mere inequalities.
First, many people consider "3 times more expensive" to be different from "3 times as expensive". I don't, because I recognize it as an idiom, but it's at least debatable.
Second, "a third as cheap" is even more unclear. Many people (possibly including me) would say it means "3 times as expensive", taking "cheap" as the reciprocal of "expensive". (Would you say "twice as cheap" to mean "twice as expensive"? I wouldn't. So why would this mean 1/3 as expensive? Yet this feels too pedantic.)
Since this problem is at least partly about interpreting English, they should use standard (unambiguous) English!
After choosing an interpretation, I myself would arrange the prices on a number line, marking 0 and whichever one I wanted to start with, like
0----O----+----A
We can't yet place B or P, so we can move on to O and B. Where does B go?
In any case, none of these are mere inequalities.
Otis
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I'd noticed sloppiness in their wording, but I chose to ignore it. I've guessed their intent, based on patterns of sloppiness that I've seen for decades. (Of course, my guesses may be incorrect.)