Another quadratic based problem

Simonsky

Junior Member
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Jul 4, 2017
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So I'm going to try to work this problem now so you can see my faulty.partially correct thinking in action:

The cost of an anorak rose by £6. As a result a shop could buy five fewer anoraks for £600. If the cost of the anorak was £x before the rise, find expressions, in terms of x, for the number of anoraks which could be bought before and after the rise. Hence form an equation in x and show that it reduces to x^2 + 6x -720 =0. Solve this equation and state the original cost of the anorak.

So the number of anoraks before the rise will be 600/x and after: (600/x) - 5. So to make an equation out of that:

(600/x) -5 = 600/(x+6) then (600/x) - 600/(x+6) -5 = 0 . So now I'm thinking I need to create common denominator:

(600(x-6))/(x^2+6x) - 600x/(x^2+6x) -5 =0

(600x -3600)/(x^2 +6x) - 600x/(x^2+6x) -5 =0

(-3600/(x^2+6x)) - 5 =0

got a bit lost-if anyone can give me a nudge (throw a life belt!) that would be great-thanks
 
First, there's a little sign error.

Then, multiply by that common denominator to clear fractions.
 
Thanks-should have got there myself but I seem to run out of mental energy too soon!

Not sure of sign error but I'll still continue and see where I get:

so: -3600- 5x^2 + 30x = 0

divide by 5: -x^2 + 6x -720 = 0 so clearly I shouldn't have -x^2 so where is the sign error?-will comb through:

okay so I wrote (second line in original calculation : (600(x-6)) !!!! sign blindness still a major problem for me (slaps forehead!).

Thanks for help.
 
Just realised I haven't finished the question:

x^2+ 6x - 720= 0

(x-24)(x+30) so x = 24 which is original cost £24.
 
Just realised I haven't finished the question:

x^2+ 6x - 720= 0

(x-24)(x+30) so x = 24 which is original cost £24.
You got:

x = 24 which is original cost £24. What quantity of items did you buy at that price for total £600?
Increased price = 24 +6 = £30. What quantity of items did you buy at that price for total £600?
 
so 25 items at £24 and 20 items at £600.
That shows the condition:

The cost of an anorak rose by £6. As a result a shop could buy five fewer anoraks for £600.

has been satisfied.

So your calculations are probably correct.
 
It seems that you do have some mistakes (and luckily got the correct answer)

(600/x) - 600/(x+6) -5 = 0. (600(x-6))/(x^2+6x) - 600x/(x^2+6x) -5 =0 1st mistake.

(-3600/(x^2+6x)) - 5 =0 so -3600- 5x^2 + 30x = 0. Note that the signs in (+x^2 + 6x) are the same in the 1st equation but in the 2nd equation the signs are now different (-5x^2+30x)!! You need to catch does errors because the same must remain the same (both + or both -)

Please go back and fix these two errors.
 
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