metal alloy that is 18.25% copper to make jewelry. How many ounces of 14% alloy must be mixed with 21% alloy to form 56 ounces of desired alloy?

Question

find amount of alloy need for 56 ounces

Answer 1

Look Tim,

This is a typical word --> math problem. Solving such problems requires, mostly, just the technique of translating the English statement into a mathematical one. The solution to the math problem is usually then quite easy!

So then ---

Always ask yourself for problems like this, "What do I start with?"

The phrase "How many ounces" is your clue. That translates into X ounces of 14% alloy (you use the variable "X" to stand for the eventual answer, which you don't know YET.).

Next, consider what you need to keep track of during the proposed action of the problem. Everything you are given is in terms of copper content (if it says "14% alloy", since there's no other metals mentioned, you may safely ASSUME that that means 14% copper, and so on). So what you need to keep track of, is the copper amounts.

So how do you do that? The copper amount of any material in the problem is just the total MASS of the material, times its COPPER DECIMAL FRACTION.

So 14% copper means 0.14 decimal fraction copper, and so on.

So now let's set up the math accounting for the copper.

One additional thing important you need to recognize before starting is, that TOTAL MASS can't change in any problem! Starting total mass = ending total mass !!

So, if you use X ounces of the 14% alloy, and end up with 56 ounces total product, you must have used (56 - X) ounces of the 21% alloy, right? Because : ((56 - X) + X = 56)

OK, now you're ready to write the accounting statement for the copper:

From the 14% alloy, you have X * 0.14 ounces copper. [total mass * fraction copper = amount of copper only]

From the 21% alloy, you have (56 - X) * 0.21 ounces copper.

And you must end up with 56 ounces of 18.25% alloy, that contains 56 * 0.1825 ounces copper.

OK, you're ready to write the math equation now, to track the copper:

(X * 0.14) + ((56 - X) * 0.21) = 56 * 0.1825

That simply says, the copper that you _start_ with (in the two sources) is the same as the copper that you _end up_ with.

Solve the equation:

0.14X + 11.76 - 0.21X = 10.22

-0.07X = -1.54

X = 22

Please note that the three important things to remember are:

1) Decide what "thing" to track in a problem. It might be a mass, length, time, etc. depending on the problem. If you track the wrong thing, you'll simply end up with an equation you can't solve; so go back and try tracking something else!

2) Start with whatever thing(s) the problem says to start with.

3) Use a variable (or more than one variable, in more complicated problems -- but you won't see those for a while, I'm guessing) for the quantity of the "thing" that you don't know yet.

4) Use common sense to avoid making unneeded variables! For example above, the amount of 21% alloy didn't need to be another variable, because you could use the Law of Conservation of Mass to express it in terms of X, the variable you were already using.

5) Set up an equation to account for the "thing" you're tracking.

6) Solve the equation.

7) Check what you did again, to make sure that you don't have to do any further calculations. For example, let's say, if you set up in terms of a variable for distance, but you needed (for the answer) a speed, you would have to use your intermediate result for distance to calculate the final answer for speed.

8) Write your answer; don't forget proper UNITS and any ROUNDING required to satisfy the requirements for showing proper precision (if you don't know what that's all about yet, don't fret; you'll learn it eventually).

Hope this helps you. Please feel free to give me feedback!