Question

There are bricks of silver and bricks of gold. When 5 silver bricks and 2 gold bricks are placed on a scale, the weight is 119 ounces. When 4 silver bricks and 11 gold bricks are placed a scale the weight is 302 ounces. How much does each one weigh?

Answer 1

The weight of one gold brick is 15 ounces and the weight of one silver brick is 22 ounces.

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`

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`

Now, multiplying equation 1 by 4 and equation 2 by 5 we get;

`4(5x+2y)=119*4\\\\20x+8y=476\ \ \ \ \ equation\ 3`

`5(4x+11y)=302*5\\\\20x+55y=1510\ \ \ equation\ 4`

Now subtract equation 3 from equation 4, we get;

`(20x+55y)-(20x+8y)=1510-476\\\\20x+55y-20x-8y=1034\\\\47y=1034\\\\y=(1034)/(47)\\\\y=22`

On substituting yhe value of y in equation 1, we get;

`5x+2y=119\\\\5x+2*22=119\\\\5x+44=119\\\\5x=119-44=75\\\\x=(75)/(5)\\\\x=15`

Thus the weight of one gold brick is 15 ounces and the weight of one silver brick is 22 ounces.