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Attention: People good at Algebra

Posted by Ddude the Insane , Dec 17 2012 · 168 views

Does anyone have advice for solving word problems where you know how much more money two people need to buy something, and know that their money together can buy one of an item, but don't know the cost of the item? These ones always get me...
 
Problem I'm dealing with at the moment:
 
Kristin and her sister Alison both want to buy the same bicycle. Kristin needs $73 more to afford the bike and Allison needs $65 more. If they combine their money, they will have just enough to buy one bicycle that they could share. What is the cost of the bicycle?
 
All help appreciated! ...for the record I'm pretty good at math, I just hate word problems :P

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$138. If both had enough for their own bike, they would have 2x dollars. However, they only have x dollars. Ergo, the amount they need is equal to x. They need $65+$73. 65+73=138.

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Ddude the Insane
Dec 17 2012 11:05 PM

$138. If both had enough for their own bike, they would have 2x dollars. However, they only have x dollars. Ergo, the amount they need is equal to x. They need $65+$73. 65+73=138.

See, that was what I'd been thinking, but that seemed too simple...

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Occam's Razor, mi amigo. "Other things being equal, a simpler explanation is better than a more complex one."

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Colette Llyan
Dec 17 2012 11:22 PM

What Xaeraz said, all of it. Sometimes, if things seem too simple; there's no real reason, it just literally is that simple. =P

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You could do it with substitution:

 

K + 73 = X

A + 65 = X

A + K = X

 

Substitute A + K in for X and you get

 

K + 73 = A + K

A + 65 = A + K

 

Which is broken down to

 

A = 73

K = 65

 

And thus

 

73 + 65 = X

 

Basically a long way to same the same thing as Xaeraz, but with more equations, and if math teachers like anything, it's equations!

 

Really, the question here is why should they combine their money and share a bike, when they should just save some more on their ends and wait a little while.  Maybe have an equation comparing their incomes to calculate who will be able to purchase the last bike availible first, so they can ride it while the other is left weeping on foot.  :evilgrin:

 

:music:

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I hate algrebra with a vengeance, but this one was pretty simple.

 

I hate math in general. It doesn't mean I'm necessarily bad at it, no. I can get straight A's. It just takes me a long time to figure it all out and write it down.

 

Which is why I hate math.

 

I took Business Math as an elective this year, but that's pretty elementary.

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