Question 1161874
<br>
Here is a non-algebraic method for solving mixture problems like this.<br>
If you understand this method, it will get you to the answer much faster and with less work than the traditional algebraic method shown by the other tutor.<br>
Think of the problem this way:<br>
You are starting with a 60% copper alloy and you are adding 10% copper alloy, reducing the percentage of copper; you stop when the percentage reaches 20%.<br>
Now model that with numbers on a number line.  You are starting at 60 and heading towards 10, but you stop when you get to 20.<br>
What fraction of the distance have you gone?  From 60 to 10 is a difference of 50, the distance you went, from 60 to 20, was 40.  The fraction is 40/50 = 4/5.<br>
That means 4/5 of the final alloy has to be the 10% alloy that you are adding.<br>
So the 400 ounces you started with is 1/5 of the final alloy; that means the 4/5 of the final alloy that you added is 4*400 = 1600 ounces.<br>
The words of explanation make this sound like a lengthy process; but it is not.  Without the words of explanation, here is the complete solution:<br>
(1) 60 to 10 is 50; 60 to 20 is 40; 40/50 = 4/5
(2) 4/5 of the final alloy is the 10% alloy you are adding; that's 4 times the 400 ounces you started with -- so 1600 ounces.<br>