5/7 + 5/14 = 1.07142857143
you can round that to 1.1
Answer:
![(x,y,z)=(1477, 1464, 1437)](https://tex.z-dn.net/?f=%28x%2Cy%2Cz%29%3D%281477%2C%201464%2C%201437%29)
Step-by-step explanation:
Consider the selling of the units positive earning and the purchasing of the units negative earning.
<h3>Case-1:</h3>
- Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y
- Mr.A earns Rs6000
So, the equation would be
![3x + 5y - 4z = 6000](https://tex.z-dn.net/?f=3x%20%20%2B%20%205y%20-%204z%20%3D%206000)
<h3>Case-2:</h3>
- Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z
- Mr B neither lose nor gain meaning he has made 0₹
hence,
![2x - 3y + z = 0](https://tex.z-dn.net/?f=2x%20%20%20-%203y%20%20%2B%20%20z%20%3D%200)
<h3>Case-3:</h3>
- Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z
- Mr.C earns 13000₹
therefore,
![- x + 4y + 6z = 13000](https://tex.z-dn.net/?f=%20-%20x%20%20%20%20%2B%204y%20%20%2B%20%206z%20%3D%2013000)
Thus our system of equations is
![\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D3x%20%20%2B%20%205y%20-%204z%20%3D%206000%5C%5C2x%20%20%20-%203y%20%20%2B%20%20z%20%3D%200%5C%5C%20-%20x%20%20%20%20%2B%204y%20%20%2B%20%206z%20%3D%2013000%5Cend%7Bcases%7D)
<u>Solving </u><u>the </u><u>system </u><u>of </u><u>equations</u><u>:</u>
we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:
![\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\end{cases}\\\begin{cases}2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D3x%20%20%2B%20%205y%20-%204z%20%3D%206000%5C%5C2x%20%20%20-%203y%20%20%2B%20%20z%20%3D%200%5Cend%7Bcases%7D%5C%5C%5Cbegin%7Bcases%7D2x%20%20%20-%203y%20%20%2B%20%20z%20%3D%200%5C%5C%20-%20x%20%20%20%20%2B%204y%20%20%2B%20%206z%20%3D%2013000%5Cend%7Bcases%7D)
Now solve the equation accordingly:
![\implies\begin{cases}11x-7y=6000\\-13x+22y=13000\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%5Cbegin%7Bcases%7D11x-7y%3D6000%5C%5C-13x%2B22y%3D13000%5Cend%7Bcases%7D)
Solving the equation for x and y yields:
![\implies\begin{cases}x= \dfrac{223000}{151}\\\\y= \dfrac{221000}{151}\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%5Cbegin%7Bcases%7Dx%3D%20%5Cdfrac%7B223000%7D%7B151%7D%5C%5C%5C%5Cy%3D%20%5Cdfrac%7B221000%7D%7B151%7D%5Cend%7Bcases%7D)
plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,
![\implies z= \dfrac{217000}{151}](https://tex.z-dn.net/?f=%5Cimplies%20z%3D%20%5Cdfrac%7B217000%7D%7B151%7D%20)
Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437
Answer:
The value of x would be
or ![\frac{3}{8}z](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B8%7Dz)
Step-by-step explanation:
Given,
x tons of 10% gravel G mixture is mixed with y ton of 2% gravel G to obtain 5% gravel mixture,
Thus, gravel G in x ton + gravel in y ton = gravel G in the resultant mixture,
⇒ 0.1x + 0.02y = 0.05(x+y),
0.1x - 0.05x = 0.05y - 0.02y
0.05x = 0.03y
![\implies x = \frac{0.03}{0.05}y=\frac{3}{5}y----(1)](https://tex.z-dn.net/?f=%5Cimplies%20x%20%3D%20%5Cfrac%7B0.03%7D%7B0.05%7Dy%3D%5Cfrac%7B3%7D%7B5%7Dy----%281%29)
Now, resultant mixture is z ton,
i.e. ![z=x+y](https://tex.z-dn.net/?f=z%3Dx%2By)
![\implies y = z - x](https://tex.z-dn.net/?f=%5Cimplies%20y%20%3D%20z%20-%20x)
From equation (1),
![x=\frac{3}{5}(z-x) = \frac{3}{5}z-\frac{3}{5}x](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B5%7D%28z-x%29%20%3D%20%5Cfrac%7B3%7D%7B5%7Dz-%5Cfrac%7B3%7D%7B5%7Dx)
![x+\frac{3}{5}x=\frac{3}{5}z](https://tex.z-dn.net/?f=x%2B%5Cfrac%7B3%7D%7B5%7Dx%3D%5Cfrac%7B3%7D%7B5%7Dz)
![\frac{8}{5}x=\frac{3}{5}z](https://tex.z-dn.net/?f=%5Cfrac%7B8%7D%7B5%7Dx%3D%5Cfrac%7B3%7D%7B5%7Dz)
![x=\frac{3}{8}z](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B8%7Dz)
It might either be a right triangle or a cute triangle