Question

the sum of three numbers 52. the third number is twice the second, and is also 2 less than 3 times the first. find the first number​

Answer 1

Let the three numbers be a, b and c.

Given:

• Sum of the three numbers is 52
• Third number is twice the second
• Third number is 2 less than thrice the first number

Solution:

Using the given conditions, we can write

• a + b + c = 52 ... (1)
• c = 2 b ... (2)
• c = 3 a - 2 ... (3)

From (2), we get     b = c/2

From (3), we get     a = (c + 2)/3

Substituting the values of a and b in (1), we get

•     (c + 2)/3 + c/2 + c = 52
• ⇒ (2 c + 4 + 3 c + 6 c)/6 = 52
• ⇒ 11 c + 4 = 312
• ⇒ 11 c = 308
• ⇒ c = 28

Putting c = 28 in (2), we get     b = 14

Putting c = 28 in (3), we get     a = 10

Answer: The three numbers are 10, 14 and 28.