Answer:
The weight of one gold brick is 15 ounces and the weight of one silver brick is 22 ounces.
Step-by-step explanation:
Given,
Weight of 5 silver bricks and 2 gold bricks = 119 ounces.
And Weight of 4 silver bricks and 11 gold bricks = 302 ounces.
We have to find out weight of each type of brick.
Solution,
Let the weight of 1 silver brick be x.
And the weight of 1 gold brick be y.
Since the weight of 5 silver bricks and 2 gold bricks is 119 ounces.
So we can frame it in equation as;
![5x+2y=119\ \ \ \ \ equation\ 1](https://tex.z-dn.net/?f=5x%2B2y%3D119%5C%20%5C%20%5C%20%5C%20%5C%20equation%5C%201)
Again,
The weight of 4 silver bricks and 11 gold bricks is 302 ounces.
So we can frame it in equation as;
![4x+11y=302\ \ \ \ \ equation\ 2](https://tex.z-dn.net/?f=4x%2B11y%3D302%5C%20%5C%20%5C%20%5C%20%5C%20equation%5C%202)
Now, multiplying equation 1 by 4 and equation 2 by 5 we get;
![4(5x+2y)=119\times4\\\\20x+8y=476\ \ \ \ \ equation\ 3](https://tex.z-dn.net/?f=4%285x%2B2y%29%3D119%5Ctimes4%5C%5C%5C%5C20x%2B8y%3D476%5C%20%5C%20%5C%20%5C%20%5C%20equation%5C%203)
![5(4x+11y)=302\times5\\\\20x+55y=1510\ \ \ equation\ 4](https://tex.z-dn.net/?f=5%284x%2B11y%29%3D302%5Ctimes5%5C%5C%5C%5C20x%2B55y%3D1510%5C%20%5C%20%5C%20equation%5C%204)
Now subtract equation 3 from equation 4, we get;
![(20x+55y)-(20x+8y)=1510-476\\\\20x+55y-20x-8y=1034\\\\47y=1034\\\\y=\frac{1034}{47}\\\\y=22](https://tex.z-dn.net/?f=%2820x%2B55y%29-%2820x%2B8y%29%3D1510-476%5C%5C%5C%5C20x%2B55y-20x-8y%3D1034%5C%5C%5C%5C47y%3D1034%5C%5C%5C%5Cy%3D%5Cfrac%7B1034%7D%7B47%7D%5C%5C%5C%5Cy%3D22)
On substituting yhe value of y in equation 1, we get;
![5x+2y=119\\\\5x+2\times22=119\\\\5x+44=119\\\\5x=119-44=75\\\\x=\frac{75}{5}\\\\x=15](https://tex.z-dn.net/?f=5x%2B2y%3D119%5C%5C%5C%5C5x%2B2%5Ctimes22%3D119%5C%5C%5C%5C5x%2B44%3D119%5C%5C%5C%5C5x%3D119-44%3D75%5C%5C%5C%5Cx%3D%5Cfrac%7B75%7D%7B5%7D%5C%5C%5C%5Cx%3D15)
Thus the weight of one gold brick is 15 ounces and the weight of one silver brick is 22 ounces.