Question

Three times the smallest of three consecutive odd numbers decreased by 7 equals twice the largest one. Find the numbers​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The required numbers are 15, 17, 19

$\mathfrak{\large{\underline{\underline{Explanation:-}}}}$

Let the three consecutive odd numbers be x + 1, x + 3, x + 5

Three times the number and decreased by 7 = 3(x + 1) - 7 = (3x + 3) - 7 = 3x + 3 - 7 = (3x - 4)

Twice the largest number = 2(x + 5) = (2x + 10)

According to the question :-

Equation formed :- $\boxed{\tt{(3x - 4) = (2x + 10)}}$

$\tt{\implies{3x - 4 = 2x + 10}}$

$\tt{\implies{3x - 2x = 10 + 4}}$

$\tt{\implies{x = 14}}$

Now we can find the numbers

(x + 1) = (14 + 1) = 15

(x + 3) = (14 + 3) = 17

(x + 5) = (14 + 5) = 19

Therefore the required numbers are 15, 17, 19

$\mathfrak{\large{\underline{\underline{Verification:-}}}}$

$\tt{\implies{3(15) - 7 = 2(19)}}$

$\tt{\implies{45 - 7 = 38}}$

$\tt{\implies{38 = 38}}$