Let and be the amounts of available alloy (AA) and pure magic steel that are used, so we also have
DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of
For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel; kg of it will contain kg of gold, kg of silver, and kg of steel. Each kg of magic steel of course contributes 1 kg of steel; kg of it will contribute kg of steel.
Then the dwarves need
• total gold:
• total silver:
• total steel:
Solve for and . The first two equations are consistent and give , and substituting this into the third we find . So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.
Come on now, Tayala !
What if I say to you:
"Start with 3 cows, take away 7 cows, and then add 14 cows. How many are there ?"
Don't let the little 't' scare you. It doesn't matter one bit what 't' really is. It can be
a number, a teacher, a tiger, or a teacup. Whatever it is, you start with 3 of them,
take away 7 of them, and then add on 14 of them. How many are there ?
Hint: If there are not ten of them, then go back and look at the cows again.
For each, divide the amount by the number of wings
7 divided by 8: 0.875 = $0.88 per wing
10 divided by 12: 0.8333 = $0.83 per wing
17 divided by 20: 0.85 = $0.85 per wing
Looking at each result, the middle one (the $10 for 12 wings) is the best deal