Respuesta :
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;
[tex]5x+2y=119\ \ \ \ \ equation\ 1[/tex]
Again,
The weight of 4 silver bricks and 11 gold bricks is 302 ounces.
So we can frame it in equation as;
[tex]4x+11y=302\ \ \ \ \ equation\ 2[/tex]
Now, multiplying equation 1 by 4 and equation 2 by 5 we get;
[tex]4(5x+2y)=119\times4\\\\20x+8y=476\ \ \ \ \ equation\ 3[/tex]
[tex]5(4x+11y)=302\times5\\\\20x+55y=1510\ \ \ equation\ 4[/tex]
Now subtract equation 3 from equation 4, we get;
[tex](20x+55y)-(20x+8y)=1510-476\\\\20x+55y-20x-8y=1034\\\\47y=1034\\\\y=\frac{1034}{47}\\\\y=22[/tex]
On substituting yhe value of y in equation 1, we get;
[tex]5x+2y=119\\\\5x+2\times22=119\\\\5x+44=119\\\\5x=119-44=75\\\\x=\frac{75}{5}\\\\x=15[/tex]
Thus the weight of one gold brick is 15 ounces and the weight of one silver brick is 22 ounces.
