he difference of 1/2 of one number and 2/3 of another number is equal to 2. If the first number were to decrease by 5/6 of it, and the second number were to increase by 1/6 of it, their sum would be equal to 59. Find the two numbers.

Answer:the first number is 60the second number is 42Step-by-step explanation:If we let x and y represent the first and second numbers, respectively, then the first sentence of the problem statement tells us ...   (1/2)x - (2/3)y = 2The second sentence of the problem statement tells us ...   (1 -5/6)x +(1 +1/6)y = 59SolutionMultiplying the first equation by 6 gives ...   3x -4y = 12Multiplying the second equation by 6 gives ...   x + 7y = 354Solving the second equation for x gives ...   x = 354 -7ySubstituting that into the first equation gives ...   3(354 -7y) -4y = 12   1050 = 25y . . . . . . . . subtract 12-25y   42 = y . . . . . . . . . . . .  divide by 25Then we can find x using its equation ...   x = 354 -7·42 = 60The first number is 60; the second number is 42.