Question

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 200 grams of an alloy containing 45% copper with 120 grams of an alloy

containing 75% copper.
Answer the questions below. Do not do any rounding.
A) how many grams of copper are in he resulting mixture?


B) what % of the resulting mixture is copper?

Answer 1

If u don’t understand I’m sorryyy

Answer 2

A: 180 grams

B: 56.25%

Explanation:

Since the first alloy is 200 grams, and is 45% copper, we can calculate how many grams are copper by calculating 45% of 200 grams.

We do this by converting 45% to a decimal, which can be done by dividing by 100. This results in the decimal value 0.45, and now we take this decimal value and multiply it by the 200 grams (total value), doing this gets us a value of 90 grams

If we do the same process to the 120 grams with 75% copper we get: 120 * (75/100) = 90

So 90 grams of copper in the first alloy, and 90 grams of copper in the second alloy.

This means there will be 180 grams of copper in the alloy.

Now to find how much % are in this mixture, we do a similar process in which we calculate x% of the mixtures.

In the first mixture we determined 90 grams was 45% of it, because 200 * (45/100) = 90

In other words:
`200*0.45=90`

But if we were to divide both sides by 90, see how we isolate the percentage in decimal form?
`0.45 = (90)/(200)`

Now to get it back into percentage form, we would just multiply both sides by 100.

This is the essence of calculating percentage given a part and a whole, you would generally just do:
`100((part)/(whole))`

In our mixture, part of it will be copper (180 grams), and the whole will be 120 + 200 grams which is just 320.

Now dividing the copper by the total amount, we get:
`(180)/(320) = 0.5625`

Now multiplying this value by 100 (since it's in decimal form), we get:
`56.25\%`