Variation problems isn't so bad, once you get the hang of it. But then they want you to move on to setting up and solving word problems. These generally fall into two categories: the ones where they want you to find the value of "k", and the ones where they want you to find some other value, but only after you've found "k" first. Here are some examples:
- If y varies directly as x2, and y = 8 when x = 2, find y when x = 1.
- Since this is direct variation, the formula is "y = kx2". The reason they've given me the data point(x, y) = (2, 8) is that I have to be able to find the value of "k". So I'll plug in the information they've given me, and solve for k:
- y = kx2
8 = k(22)
8 = 4k
2 = k
- y = 2x2
y = 2(1)2
y = 2×1
y = 2
- If y varies directly as x and z, and y = 5 when x = 3 and z = 4,
then find y when x = 2 and z = 3.
- Translating the formula from English to math, I get:
- y = kxz
- 5 = k(3)(4)
5 = 12k
5/12 = k
- y = ( 5/12)xz
y = ( 5/12)(2)(3)
y = ( 5/12)(6)
y = 5/2