Alloy #13 contains 7% gold, if means that if we need 2.7kg of this alloy, we will have to use a certain amount of gold. Multiply the percent of gold times the mass of alloy to find how much gold we need:
![2.7kg\cdot7\%=0.189kg](https://tex.z-dn.net/?f=2.7kg%5Ccdot7%5C%25%3D0.189kg)
It means that we need 0.189kg of gold.
The alloy we have contains 21% of gold. That means that for every 100kg of alloy there are 21kg of gold, use this ratio to find the mass of alloy we need:
![0.189kgGold\cdot\frac{100kgAlloy}{21kgGold}=0.9kgAlloy](https://tex.z-dn.net/?f=0.189kgGold%5Ccdot%5Cfrac%7B100kgAlloy%7D%7B21kgGold%7D%3D0.9kgAlloy)
It means that we need 0.9kg of that alloy.
To find how much magic steel we need, we just have to substract this mass from the mass of Alloy #13:
![2.7kg-0.9kg=1.8kg](https://tex.z-dn.net/?f=2.7kg-0.9kg%3D1.8kg)
It means that we need 1.8kg of magic steel.
The answer is: The dwarves need 1.8 kg of magic steel and 0.9 kg of their alloy in order to get 2.7 kg of Dragon Alloy #13.