Question

Alloy A is composed of 3 parts gold and 1 part silver. Alloy B is composed of 1 part good and 3 parts silver. When combined, the allow mixture has 15 g of gold and 9 g of silver. How many grams does each alloy weigh?

Answer 1

Alloy A weighs 18 g

Alloy B weighs 6 g

Explanation:

Let the weight of Alloy A be "x" g and Alloy B be "y" g.

It is given that Alloy A is composed of 3 parts gold and 1 part silver and Alloy B is composed of 1 part good and 3 parts silver.

The total gold is given by,

=
`((3)/(4))(x) + (1)/(4)(y)` = 15 g

The total silver is given by,

=
`((1)/(4))(x) + (3)/(4)(y)` = 9 g

adding both the equations we get,

`x+y = 24`

and subtracting we get,

`x-y = 12`

Thus, by solving we get,

x=18 and y=6.