One number is 6 times another number. the sum of the two numbers is 84. find the two numbers.

Let’s call our “one number” x and “another number” y. x is six times y, which we can express with the equation x = 6y. We also know that their sum is 84, a fact which we can write as x + y = 84. Well, x is worth 6 y’s, and if we add another y onto that, we get a total of 7 y’s, or 7y. So 7y = 84, and the only number y could be to make that true is 12, so y = 12. And since x = 6y, x must by 6 • 12, or 72.