Final answer:
Using the original ratio 5:6 and the new ratio 7:8 with the added 8 to each number, we set up a proportion, cross-multiply to find a common denominator, and solve for x to get the two numbers which are 20 and 24. Option a is the correct answer.
Step-by-step explanation:
To solve this ratio problem, we set up two equations based on the given information. Let the two numbers be 5x and 6x, which are in the ratio 5:6. If we add 8 to each of the numbers, the new numbers become (5x + 8) and (6x + 8), and these should be in the ratio 7:8.
We set up the equation:
(5x+8) / (6x+8) = 7/8
We can now cross-multiply to find a common denominator:
8(5x + 8) = 7(6x + 8)
40x + 64 = 42x + 56
After simplifying, we find:
2x = 8
x = 4
The two numbers are therefore:
5x = 5 * 4 = 20
6x = 6 * 4 = 24
Option a: 20, 24 is the correct answer.