Question

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?

Answer 1

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"