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?

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