Chapter 6.4, Problem 2LC

To determine

To calculate: amount of each alloy to create $4kg$ of an alloy containing $15\%$ gold .

Answer to Problem 2LC

one kg of first and three kg of second alloy

Explanation of Solution

Calculation:

Let’s assume $x$ kg of metal one and $y$ kg of metal two is required.

Therefore, for the final alloy of $4$ kg,

  $x+y=4$ …..(i)

Now, One alloy is $30\%$ gold and the other is $10\%$ gold and for final alloy $15\%$ gold is required.

  $\therefore 0.30x+0.10y=4\times 0.15$

  $\therefore 3x+y=6$ ….(ii)

By substituting $y$ from equation (i) into equation (ii), we get,

  $\therefore 3x+4-x=6$

  $\therefore x=1$

By substituting value of $x$ in equation (i), we get,

  $\therefore y=3$

Therefore, to get required alloy, one kg of first and three kg of second alloy is required.