he ratio of two numbers is 5 : 8 and the difference between their squares is 351. What is the sum of the numbers? Ops: A. 39 B. 48 C. 45 D. 43
Question
he ratio of two numbers is 5 : 8 and the difference between their squares is 351. What is the sum of the numbers? Ops: A. 39 B. 48 C. 45 D. 43
Solution
Let's denote the two numbers as 5x and 8x, where x is a common multiplier.
According to the problem, the difference between their squares is 351. So, we can write the equation as follows:
(8x)^2 - (5x)^2 = 351
64x^2 - 25x^2 = 351
39x^2 = 351
Solving for x, we get:
x^2 = 351 / 39
x^2 = 9
So, x = 3
Therefore, the two numbers are 5x = 53 = 15 and 8x = 83 = 24
The sum of the two numbers is 15 + 24 = 39
So, the answer is A. 39.
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