Percentage question Certain alloy contains 20% of copper and 5% of tin. How much of copper and how much tin must be added to 100kg of this alloy to get another with 30% of copper and 10% of tin?
I can't figure how to start it
 A: My list of leading questions as used in the comment section to the question:

 How much copper do the 100kg of alloy contain?

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 Now, if you add x kg of copper and y kg of tin, how much copper does the result contain?

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 If you add x kg of copper and y kg of tin, how much kg does the result have?

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 So, what is the percentage of copper in the result? This should give you one equation. You get a similar equation for the tin. Then you solve the system of two equations.

A: Given your problem statement, you have the following quantities: 20kg of copper, 5kg of tin
and 75kg of the base metal, 100kg total.
You want to add an unknown amount $x$ to the copper such that the new percentage of copper in the alloy is 30%, thus  $(20 + x) / (100 + x + y) = 0.3$. Likewise, you are looking for an amount $y$ to add to the amount of tin such that the new percent is 10%, thus $(5 + y) / (100 + x + y) = 0.1$. Likewise, you known that the base percentage is now going to be 60%, thus $75 / (100 + x + y) = 0.6$.
With some algebra you get:
$$20 + x = 0.3 (100 + x + y)$$
$$20 + x = 30 + 0.3x + 0.3y$$
$$-10 = -0.7x + 0.3y$$
$$5 + y = 0.1 (100 + x + y)$$
$$5 + y = 10 + 0.1x + 0.1y$$
$$-5 = 0.1x - 0.9y$$
Which will give you the following system:
$$\pmatrix{ -10 \\ -5 } = \pmatrix{ -0.7 & 0.3 \\ 0.1 & -0.9} \pmatrix { x \\ y }$$
Solving it will yield:
$$\pmatrix{x \\ y } = \pmatrix{ 17.5 \\ 7.5 }$$
Thus, you would need to add 17.5kg of copper and 7.5kg of tin to get a new alloy with 30% copper, 10% tin and 60% base.
