Final answer:
To find the amount that must be added to 2/7 + 3/8 to have an average of 2/12, the common denominator is determined, and the equation (16/56 + 21/56 + x)/3 = 2/12 is set up and solved for x, giving the answer as -9/56.
Step-by-step explanation:
To find the amount that must be added to 2/7 + 3/8 so that the three fractions have an average of 2/12, we need to determine the common denominator. The common denominator for 7 and 8 is 56. So the fractions become 16/56 and 21/56. Now, we can set up the equation (16/56 + 21/56 + x)/3 = 2/12 and solve for x. Multiplying both sides of the equation by 3, we get 16/56 + 21/56 + x = 6/12. Combining like terms, we have (16 + 21 + 56x)/56 = 1/2. Solving for x, we get 37 + 56x = 28. Subtracting 37 from both sides, we get 56x = -9. Dividing by 56, we find x = -9/56.