After defeating the fire breathing dragon, the knight decides to celebrate his victory

Question

with a celebratory goblet made out of Dragon Alloy #17, which is 36% gold, 9%
silver, and 55% magic steel. The dwarves have Dragon Alloy #11, which is 36% gold,
28% magic steel, and the rest silver. They also have Dragon Alloy #15, which is 36%
gold and 64% magic steel. How many grams of each alloy should the dwarves
combine to get 1 kg of Dragon Alloy #17?

The dwarves have to mix_grams of Dragon Alloy # 11 and_grams of Dragon Alloy # 15.

Answer 1

if they use x grams of #11 and y grams of #15, then since the gold content is the same in all the alloys, you just need
28x+64y = 55(x+y)
y = 3x

So just mix #11 and #15 in the ratio 1:3
That is, 250g #11 and 750g #15

Answer 2

They want to have 1000 g of #17, so it must contain
360 g of gold
90 g of silver
550 g of magic steel

#15:
gold --- 36% , silver ---- 0% , magic steel -- 64%
#11:
gold --- 36% , silver -- 36% , magic steel -- 28%

suppose they use x g of the #15
and y g of #11, so they have

in gold: .36x + .36y = 360
x + y = 1000

for silver:
0x + .36y = 90
y = 250 , so x = 750 <---- they need 750 g of the #15, and 250 g of the #11

Does this check out?

the 750g of #15 contains: 270 gold, 0 silver, 480 magic
the 250g of #11 contains: 90 gold, 90 silver, 70 magic
total gold = 360
total silver = 90
total magic steel = 550 , for a total of 1000 g, as needed.

my answer is correct

Answer 3

looks like I went from Toronto to Niagara Falls by
Toronto -----> Detroit
Detroit ---> Cleveland
Cleveland ---> Buffalo
Buffalo ----> Niagara Falls , but I got there !