Question

A treasury has 500 7-ounce weights, 500 11-ounce weights, and a balance. a foreign dignitary arrives with a gold bar, claiming it to weigh 500 ounces. can the treasury determine whether the dignitary is telling the truth? if so, how?

Answer 1

Yes the treasury can determine whether the gold bar is really weighing 500 ounces.

We can use the equation:

7 x + 11 y = 500

where x is the amount of the 7 ounce weights while y is the amount of 11 ounce weights.

We know that x and y should be whole numbers therefore this is solved through trial and error.

By trial and error I got:

x = 7 and y = 41

So that;

7 * 7 + 11 * 41 = 500

49 + 451 = 500

500 = 500

Hence they can use 41 11-ounce weights and 7 7-ounce weights to test