The sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2. Find the number

The sum of a number, 1/6 of that number, 2 1/2 of that number, and 7 is 12 1/2. Find the number?

the number is 2.409

Step-by-step explanation:

based on the question;

let the number N

1/6 of N = (1/6) N

21/2 of N = (5/2) N

now, the sum of a number (N) 1/6 of that number (1/6) N, (5/2) N and 7 will be expressed as

N + (1/6) N + (5/2) N + 7 = 12 1/2

N + N/6 + 5N/2 + 7 = 25/2

find the lcm of the equation

we have;

(6N + N + 15N + 42) / 6 = 25/2

(22N + 42) / 6 = 25/2

Using cross multiplication we have

44N + 84 = 150

Collecting the like terms

44N = 150 - 84

44N = 106

Divide both sides by 44

44N/44 = 106/44

N = 2.409