Answer: Time taken by Ximena to paint the fence alone = 24 hours
Time taken by Candice to paint the fence alone = 12 hours
Step-by-step explanation:
Let x= Time taken by Ximena to paint the fence alone .
Time taken by Candice to paint the fence alone = x-12
As per given , we have
![\dfrac{1}{x}+\dfrac{1}{x-12}=\dfrac{1}{8}\\\\\Rightarrow\ \dfrac{x-12+x}{x(x-12)}=\dfrac{1}{8}\\\\\Rightarrow\ 8(2x-12)=x^2-12x\\\\\Rightarrow\ 16x-96=x^2-12x\\\\\Rightarrow\ x^2-12x-16x+96=0\\\\\Rightarrow\ x^2-28x+96=0\\\\\Rightarrow\ x^2-4x-24x+96=0\\\\\Rightarrow\ x(x-4)-24(x-4)=0\\\\\Rightarrow\ (x-4)(x-24)=0\\\\\Rightarrow x=4, 24](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7Bx%7D%2B%5Cdfrac%7B1%7D%7Bx-12%7D%3D%5Cdfrac%7B1%7D%7B8%7D%5C%5C%5C%5C%5CRightarrow%5C%20%5Cdfrac%7Bx-12%2Bx%7D%7Bx%28x-12%29%7D%3D%5Cdfrac%7B1%7D%7B8%7D%5C%5C%5C%5C%5CRightarrow%5C%208%282x-12%29%3Dx%5E2-12x%5C%5C%5C%5C%5CRightarrow%5C%2016x-96%3Dx%5E2-12x%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2-12x-16x%2B96%3D0%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2-28x%2B96%3D0%5C%5C%5C%5C%5CRightarrow%5C%20x%5E2-4x-24x%2B96%3D0%5C%5C%5C%5C%5CRightarrow%5C%20x%28x-4%29-24%28x-4%29%3D0%5C%5C%5C%5C%5CRightarrow%5C%20%28x-4%29%28x-24%29%3D0%5C%5C%5C%5C%5CRightarrow%20x%3D4%2C%2024)
if x= 4
Time taken by Ximena = 4 hours
Time taken by Candice = 4-12 hours =-8 hours which is not possible. (time cannot be negative)
Therefore, x= 24
Such that
Time taken by Ximena to paint the fence alone = 24 hours
Time taken by Candice to paint the fence alone = 24-12=12 hours
Answer:
Cola bottles are cheaper. Mark me brainliest!
Step-by-step explanation:
First things first, write out your equation without the substitution.
2x+ 2y= 10
Now, put in the substitution.
2x+ 2• 2= 10
Combine like terms.
2x+ 4= 10
Now that your equation it simplified, you need to reverse the problem and put everything on the other side.
2x+ 4= 10
- 4 - 4
2x = 6
2x=6
— —
2 2
X= 3
So the final answer is x=3