Hi
I hope someone can shed some light on this question in my workbook. It is a holiday week and I can ask my teacher until tuesday - I'm going mad.

You buy 12 dollars worth of apples. They are kind of small so the cashier gives you two extra for free. This reduces the price per dozen by exactly 1 dollar. How many apples did you get for 12 dollars?

ok, I know the answer in the back of the book says 18 apples, but how??

any help much appreciated

Here's how I set it up:

Let A = original number of apples worth $12.
So the cashier gives you A+2 apples.

Now the original price in dollars per apple will be 12/A, and the original price in dollars per dozen apples will be 144/A. Ok so far?

Likewise the final price in dollars per dozen apples will be 144/(A+2). Right?

So we can write this equation:
144/(A+2) = 144/A - 1

I'll stop here and let you work out the rest. It will yield a quadratic equation with two roots, one of which is positive (the answer) and one of which is negative (to be discarded, because "negative apples" is meaningless).

Let me know if you want to see the complete solution. Good luck!

And welcome to AnswerPool!!

Hello K_S,
in order to solve a Maths question, it is always a good idea to formulate an equation of some sort with the information given.

Here we have apples bought for twelve dollars
two extra given
and that reduces the price by one dollar overall.

Let us assume original amount of apples to be x
and price per dozen of apples to be y

Putting it simply,
12/x=y
leading to xy=12 ---eq1

and consequently, we have
x + 2 => 12(y - 1)
which gives us
12/(x+2)= y - 1
or
(y - 1).(x + 2) = 12 ---eq2

Now solve quadratically.

Pin~Jinx / anarchist

consequently, we have
x + 2 => 12(y - 1)
which gives us
12/(x+2)= y - 1
or
(y - 1).(x + 2) = 12 ---eq2

HUH?

Did you mean (x + 2)/12 = y - 1?

I couldn't get into my post above, but I also think that your equations are incorrectly reasoned.

Let me finish the solution I outlined above:

144/(A+2) = 144/A - 1
Multiply both sides by A(A+2):
144A = 144(A+2) - A(A+2)
Expand:
144A = 144A + 288 -A^2 - 2A
Collect terms:
A^2 + 2A - 288 = 0
Factor:
(A+18)(A-16) = 0
The roots are: A = -18 and A = 16
Discard the negative root as explained earlier, leaving A=16.

(If you couldn't factor the expression, you could derive the roots using the quadratic formula instead.)

Remember A is the original number of apples worth $12.
So for $12 you actually got A+2 = 16+2 = 18 apples, which is the answer.

Pin~Jinx's formulation forgets to convert from units to dozens. And though not wrong to use two variables, I find it simpler here to use one variable and one equation.

Professor: I tried with one variable and with two variables, but I was too sleepy to deal with the big number 144 and the conversion to dozens. Fortunately, in real life I have never seen two more pieces of fruit thrown in, thereby reducing the price/dozen; instead, I have seen the price sometimes lowered, less often now than previously.

no, I did not mean what you stated

just what I wrote.

How is it incorrectly composed, pleae?
and what's the correct version algebraicly then?