math
posted by Carly
I'm having a little trouble solving inverse variation. I have four problems  2 are solved using proportions, 2 are not  why can they not all be solved using proportions?
1. y varies inversely with x. If y = 40 when x = 16, find x when y = 5
If I use a proportion for that, I get 2, however, the answer is 128.
They solved like this: (40)(16) = 5x
x = 128
2. y varies inversely with x. If y = 7 when x = 4, find y when x = 5. If I use a proportion for that, I get 8.75, and the answer is 5.6
They solved: 7x(4) = 5y
y = 5.6
3. y varies directly with x. If y = 15 when x = 18, find y when x = 1.6. I did a proportion and got the correct answer of 1.33
4. y varies directly with x. If y = 75 when x = 25, find x when y = 25. I did a proportion and got 8.333
Could you please explain #1 and #2 and why those can't be solved using proportions, and how they solved them?

Scott
direct ... y = k x ... y1 / x1 = y2 / x2
... y1 / y2 = x1 / x2
indirect ... x y = k
... x1 y1 = x2 y2 ... x1 / x2 = y2 / y1
... a proportion will work
... but it's different than direct
... it is "inverted"
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