A completely unrelated maths problem

[togfox]

Susan, Stephen and Stephanie helped their mother to carry home the shopping. Each child had seven pieces of fruit in his or her bag a mixture of apples and oranges. Stephanie had twice as many apples as Susan and fewer oranges than Stephen. Stephen had half as many oranges as Susan. How many apples did he have?

Now, before you post, I know what the answer is ... it\'s written in small print and upside down on the page of my magazine. I don\'t want to know what the answer, I want to know how you worked out the answer. This problem, and many derivitives like it, have always escaped me and I\'d like to understand the technique behind solving such mathematical equations. Thx.

[Ydoow]

I like this. Let\'s see if I can do it...

Now that I got more o\' dat math educationomatics stuffs, I might take a more algebraic approach than I normally would.

Okay everyone has 7 fruits total, and there\'s two different types of fruit in each bag.

so x+y=7, or better yet,

a+o= 7 (apples/oranges)

a_stephanie = 2*a_susan (stephanie has twice as many apples as susan)

o_stephanie < o_stephan (stephanie has fewer oranges than stephan)

o_stephen = .5*o_susan (stephen has half as many oranges as susan)

Now we put this all together somehow...

Stephanie:

2a_susan + o = 7

Stephen:

a + .5o_susan = 7

Susan:

a + o =7

And then we assume that you must have a full integer worth of fruits (no, 1.5 apples..)

Knowing that stephen has half as many oranges as susan, and Stephanie has fewer oranges than Stephan, I\'m left to believe Susan can only have 4 or 6 oranges.

Any odd number wouldn\'t make sense, because stephen would have 2.5 or 1.5 oranges.

And if Susan had 2 oranges, then Stephen would have 1 orange, meaning Stephanie would have to have less than 1 orange.

0 is possible, but then Stephanie must have 2a_susan apples.

Meaning the equation would have to be

2a + 0 =7

2a = 7

7/2 = a - basically meaning Stephanie would need a non-integer amount of apples.

SO! Susan has 4, or 6 oranges.

Really now...I guess it\'s just guess and check. It\'s only 50/50 chance of being right.

So...let\'s assume Susan has 4 oranges.

Susan:

a + (4) =7

a=3

3+4=7

Stephen:

a + .5(4)_susan = 7

a+2=7

a=5

5+2=7

Stephanie:

2(3)_susan + o<(.5*(4)) = 7

6+(o<2)=7

o=1

6+1=7

And bam.

That sounds right to me.

I think we all do this in our head, it\'s just not so explicit (we don\'t really think a+o=7, we just push numbers around).

Honestly, if I didn\'t have paper, I would normally just guess and check while following the numbers around.

[togfox]

Yep - that\'s right - or so my magazine says when I turn it upside down. I guess working out how many oranges everyone has is as simple as 7 - a.