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Two numbers are in the ratio 5:6. If 8 is added to each of the numbers, they will be in the ratio 7:8. Find the numbers.

a. 20, 24
b. 25, 30
c. 32, 40
d. 40, 48

User Worc
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1 Answer

3 votes

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.

User Ismael Luceno
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