SOLUTION: If x varies inversely as y and x = 2 when y = 8, find x when y = 4. PLEASE HELP

Question 1011904: If x varies inversely as y and x = 2 when y = 8, find x when y = 4. PLEASE HELP

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
direct variation is y = kx

inverse variation is y = k/x

k is called the constnat of variation.

it is always the same for the particular variation problem you are trying to solve.

with direct variation, solve for k to get k = y/x.

with inverse variation, solve for k to get k = yx.

first you solve for k.

then you use k to solve for y or x.

in your problem, you are dealing with inverse variation.

the formula to use is y = k/x.

solve for k to get k = xy.

when x = 2 and y = 8, k = xy becomes k = 2*8 which becomes k = 16.

now, when x = 4, the formula of y = k/x becomes y = 16/x which becomes y = 16/4.

solve for y to get y = 16/4 = 4

when x = 4, y = 4.

when x = 2, y = 8
when x = 4, y = 4

what happened?

first of all, your constant of variation is always the same after you solve for it initially.

2 * 8 = 16
4 * 4 = 16

second of all:

when x = 2, y = 8
when x = 4, y = 4

you multiplied x by 2 and you divided y by 2.

that's an inverse relationship.

if you multiply x by 2 and you multiply y by 2, that's a direct relationship.
if you multiply x by 2 and you divide y by 2, that's an inverse relationship.

let's look at the same problem one more time, this time we'll do both direct and inverse.

you are given when x = 2, y = 8

solve for direct relationship:

direct relationship formula is y = kx.
solve for k to get k = y/x which is equal to 8/2 which is equal to 4.
when x = 4, y = kx becomes y = 4*4 which becomes y = 16.
you have:
when x = 2, y = 8
when x = 4, y = 16
y is always 4 * x because the constant of variation is 4.
k is always equal to y/x and is always equal to 4.
8/2 = 4
16/4 = 4
in this example, when you multiplied 2 by 2 to get 4 then you multiplied 8 by 2 to get 16.
that's a direct relationship.

solve for inverse relationship:

inverse relationship formula is y = k/x.
solve for k to get k = xy which is equal to 2*8 which is equal to 16.
when x = 4, y = k/x becomes y = 16/4 which becomes y = 4.
you have:
when x = 2, y = 8
when x = 4, y = 4
y is always 16/x because the constant of variation is 16.
k is always equal to xy and is always equal to 16.
2*8 = 16
4*4 = 16
in this examle, when you multiplied 2 by 2 to get 4, then you divided 8 by 2 to get 4.
that's an inverse relationship.

here's a reference on the constant of variation you might find helpful.

here's some references on variation you might find useful.

http://www.regentsprep.org/regents/math/algtrig/ate7/Direct%20Variation.htm

http://www.regentsprep.org/regents/math/algtrig/ate7/Inverse%20Variation.htm

http://www.regentsprep.org/regents/math/algtrig/ate7/variation%20practice%201.htm
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