Homework word problem

[Vay]

My homework says there are "3/4 as many teenagers as preteens". Does this mean, when x=teenagers and z=preteens, that 3x/4=z or x=3z/4? This is a word problem for linear equations. I have done it both ways, and the book supports the fact that the answer is x=3z/4 when I looked at the answer at the back of my textbook, but I thought it was 3x/4=z according to the word problem and the not intention of the writer, so I wanted to verify with you guys.

 

I think I am wrong, so how do you analyze this kind of problem involving "as"?

Edited November 15, 2011 by Vay

[Sonryu]

Well, if we let X = teenagers and Z = preteens, then since there are 3/4 as many teenagers, there are MORE preteens. So Z = (4/3)X or X = (3/4)Z.

 

 

This is backed up because Preteens = (4/3) * Teens, which supports the problem saying that there are more preteens than teens.

[Vay]

How about saying there are twice as many apples as there are oranges, so that for each orange there are 2 apples. Hence, 1 orange = 2 apples and 2 oranges= 4 apples, and so on? Is this the same?

 

There are twice as many apples as there are oranges, so does this mean for each orange there are 2 apples, so that if apples=x and oranges=y, then y=2x; 2y=4x, and etc? I think the fault might lie in my misinterpretation, or maybe the statement is ambiguous.

Edited November 15, 2011 by Vay

[John]

Let [math]x[/math] represent the number of apples and [math]y[/math] represent the number of oranges.

 

Then, if there are twice as many apples as oranges, then the number of apples ([math]x[/math]) will be two times the number of oranges ([math]y[/math]). Expressed as an equation, this means [math]x = 2y[/math].

[Vay]

Never mind, I am not thinking straight after doing my math homework for 6 hours straight, I will revisit this tomorrow. I get it when you explain it, I just have to repeat it in my head over and over again...

Edited November 15, 2011 by Vay