Math Is Fun Forum

jadewest

Member

Registered: 2021-02-20

Posts: 44

Direct, Inverse, and Joint Variations

Hello,

I need help with these two exercises.

3   If y varies directly as x and z and y is 5 when x is 3 and z is 4, find y when x is 2 and z is 3.  Show steps,

Direct => y = kx

5 = k*3

5/3 = (k*3)/3

k = 5/3

y = (5/3)x

y = (5/3)*2

y = 10/3 = 3.333...

Direct => y = kz

5 = k4

5/4 = (k*4)/4

k = 5/4

y = (5/4)z

y = (5/4)*3

y = 15/4 = 3.75    (HOW DO I NOT LOSE Z?)

9      If w varies directly with f and inversely with g and w = 5 when f = 2 and g = 7, find w when f = 4 and g = 9.

Direct => w = kf

5 = 2k

k = 5/2 = 2.5

w = 2.5 * 4

w = 10

Inverse => w = k/g

5 = k/7

k = 7*5 = 35

w = 35/9 = 3.888...9   (HOW DO I NOT LOSE G?)

Thank you so much,
Jade

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Direct, Inverse, and Joint Variations

Hi Jade

I can see why you did these like this but I don't think that's what was intended.

Try like this

Y = kxz  y = 5 when x = 3 Z = 4

That means

5 = k times 3 times 4 so k = 5/12

Try finishing it from there.

In the second w = j f/g where j is a different constant

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob