1/3 is also 2/6 and 1/2 is also 3/6 add and Timothy needs 5/6 cups
Answer:
Canadian railcars show weight figures in both imperial and metric. Canadian railways also maintain exclusive use of imperial measurements to describe train length and height in feet and train masses in short tons. Canadians typically use a mix of metric and imperial measurements in their daily lives.
Answer:
![x =-24](https://tex.z-dn.net/?f=x%20%3D-24)
Step-by-step explanation:
Given
![(\frac{2}{3})(\frac{1}{2}x + 12) = (\frac{1}{2})(\frac{1}{3}x + 14) - 3](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%7D%7B3%7D%29%28%5Cfrac%7B1%7D%7B2%7Dx%20%2B%2012%29%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%28%5Cfrac%7B1%7D%7B3%7Dx%20%2B%2014%29%20-%203)
Required
Solve for x
![(\frac{2}{3})(\frac{1}{2}x + 12) = (\frac{1}{2})(\frac{1}{3}x + 14) - 3](https://tex.z-dn.net/?f=%28%5Cfrac%7B2%7D%7B3%7D%29%28%5Cfrac%7B1%7D%7B2%7Dx%20%2B%2012%29%20%3D%20%28%5Cfrac%7B1%7D%7B2%7D%29%28%5Cfrac%7B1%7D%7B3%7Dx%20%2B%2014%29%20-%203)
Open all brackets
![\frac{2}{3}*\frac{1}{2}x + \frac{2}{3}*12 = \frac{1}{2}*\frac{1}{3}x + \frac{1}{2}*14 - 3](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%2A%5Cfrac%7B1%7D%7B2%7Dx%20%2B%20%5Cfrac%7B2%7D%7B3%7D%2A12%20%3D%20%5Cfrac%7B1%7D%7B2%7D%2A%5Cfrac%7B1%7D%7B3%7Dx%20%2B%20%5Cfrac%7B1%7D%7B2%7D%2A14%20-%203)
![\frac{2 * 1}{3 *2}x + \frac{2 * 12}{3}= \frac{1 * 1}{2 * 3}x + \frac{1 * 14}{2} - 3](https://tex.z-dn.net/?f=%5Cfrac%7B2%20%2A%201%7D%7B3%20%2A2%7Dx%20%2B%20%5Cfrac%7B2%20%2A%2012%7D%7B3%7D%3D%20%5Cfrac%7B1%20%2A%201%7D%7B2%20%2A%203%7Dx%20%2B%20%5Cfrac%7B1%20%2A%2014%7D%7B2%7D%20-%203)
![\frac{1}{3}x + \frac{24}{3}= \frac{1}{6}x + \frac{14}{2} - 3](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%20%2B%20%5Cfrac%7B24%7D%7B3%7D%3D%20%5Cfrac%7B1%7D%7B6%7Dx%20%2B%20%5Cfrac%7B14%7D%7B2%7D%20-%203)
![\frac{1}{3}x +8= \frac{1}{6}x + 7 - 3](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%20%2B8%3D%20%5Cfrac%7B1%7D%7B6%7Dx%20%2B%207%20-%203)
Collect like terms
![\frac{1}{3}x - \frac{1}{6}x =7 - 3 -8](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%20-%20%5Cfrac%7B1%7D%7B6%7Dx%20%3D7%20-%203%20-8)
![\frac{1}{3}x - \frac{1}{6}x =-4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%20-%20%5Cfrac%7B1%7D%7B6%7Dx%20%3D-4)
Solve fraction
![\frac{2-1}{6}x =-4](https://tex.z-dn.net/?f=%5Cfrac%7B2-1%7D%7B6%7Dx%20%3D-4)
![\frac{1}{6}x =-4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B6%7Dx%20%3D-4)
Multiply both sides by 6
![6 * \frac{1}{6}x =-4 * 6](https://tex.z-dn.net/?f=6%20%2A%20%5Cfrac%7B1%7D%7B6%7Dx%20%3D-4%20%2A%206)
![x =-4 * 6](https://tex.z-dn.net/?f=x%20%3D-4%20%2A%206)
![x =-24](https://tex.z-dn.net/?f=x%20%3D-24)
The problem says that the expression (3x + 5)(5x − 1) <span>represents the area of the floor of the building in square meters. Therefore, to solve this problem you have to follow the proccedure shown below.
1. First, to simplify the expression (3x + 5)(5x − 1) you must apply the distributive property. Then, you obtain:
15x</span>²-3x+25x-5
2. Then, you have:
15x²+22x-5
3. As you can see, the correct answer is the last option: 15x²+22x-5