Solving for u: 0.05 = (u)*(0.15) + (1-u)(-0.15)

[benem]

Is anyone able to show the steps in how u=2/3
I'm proving to be rusty at algebra and cannot for the life of me get u=2/3

Incase the picture doesn't work:

u*0.15+(1-u)*(-0.15)=0.005

Edit*
u*0.15+(1-u)*(-15)=0.05

Cheers

 

[benem]

Solving for u

My algebra seems to be very rusty, is able to solve for u in this equation and show the steps. Would be greatly appreciated

0.05 = (u)*(0.15) + (1-u)(-0.15)

In my notes I have that we find u=2/3 but I can't for the life of me come to that answer myself.

 

[HallsofIvy]

"u*15+ (1- u)*(-15%)" should be written as 0.15u- 0.15(1- u) since 15% is just a way of writing 0.15.
0.15u- 0.15(1- u)= 0.15u- 0.15+ 0.15u= 0.30u- 0.15.

Since you are given that this expression is equal to 0.5, you have 0.30u- 0.15= 0.5. Add 0.15 to both sides to get 0.30u= 0.65.

Divide both sides by 0.30 to find u= 0.65/0.30= 65/30= 2+ 5/30, not 2/3.

 

[ksdhart2]

There's a few "hidden" steps there, but hopefully nothing too tricky. Start with the given equation:

\(\displaystyle 0.15u+(1-u)(-0.15)=0.05\)

The middle term can then be multiplied out:

\(\displaystyle 0.15u+(-0.15+0.15u)=0.05\)

Try continuing from here and see what you get.

 

[benem]

Thank you both, it's my first time using this forum and it has proved to be a great discussion board!

 

[Steven G]

Where d'ya'll get .05 on right

Multiply by 1000:
150u - 150(1 - u) = 5
Solve for u; you should get u = 31/60.

Finally someone realized that the right hand side was .005 . Amazingly it was Denis the Menace.

 

[ksdhart2]

Well, the OP says in the text portion of the post:

Incase the picture doesn't work:

u*0.15+(1-u)*(-0.15)=0.005

But the image clearly shows 5% or 0.05. I opted for the value shown in the image, believing the 0.005 to be a typo or a misreading.

 

[benem]

That was a typo, it should have read 0.05 i.e. 5%

Thank you all for the answers