the ratio of the difference obtained by subtracting 2 from thrice a number to the sum of twice the same number and 5 is13:15.what is the number?

(3N-2)/(2N+5) = 13/15.

13(2N+5) = 15(3N-2),
26N + 65 = 45N - 30, N = 5.

Let's denote the number as "x".

According to the given information, the ratio of the difference obtained by subtracting 2 from thrice the number (3x - 2) to the sum of twice the same number and 5 (2x + 5) is 13:15.

So we can set up the equation:

(3x - 2) / (2x + 5) = 13/15

To solve for x, we will cross-multiply and solve for x:

15(3x - 2) = 13(2x + 5)

45x - 30 = 26x + 65

45x - 26x = 65 + 30

19x = 95

x = 95 / 19

x = 5

Therefore, the number is 5.

To solve this problem, let's break it down step by step:

1. Let's assume the number we're looking for is "x".
2. The difference obtained by subtracting 2 from thrice the number is 3x - 2.
3. The sum of twice the same number and 5 is 2x + 5.
4. According to the given ratio, (3x - 2) : (2x + 5) = 13 : 15.

To find the value of x, we'll set up and solve the equation:

(3x - 2) / (2x + 5) = 13 / 15

15(3x - 2) = 13(2x + 5)
45x - 30 = 26x + 65
45x - 26x = 65 + 30
19x = 95
x = 95 / 19
x = 5

Therefore, the number is 5.

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