Question

Twice the larger of 2 consecutive integers equal 15 less than 3 times the smaller

Answer 1

Let's take the first number as 'x' ( This would be the smaller number )

Let's take the second number as 'x+1' ( This would be the larger number )

I have taken x and x+1 because both these numbers are consecutive.

Twice the larger number :-

... 2 ( x + 1 )

... 2x + 2

15 less than thrice the smaller number :-

... 3x - 15

The question states that these both values are equal. Hence,

... 2x + 2 = 3x - 15

... 2 + 15 = 3x - 2x

... 17 = x

The value of 'x' is 17

( The smaller number is 17 )

Larger number :-

... x + 1

... 17 + 1

... 18

Hence, the numbers are 17 and 18.

Hope my answer helps!!

Answer 2

the two integers are 17 and 18

Explanation:

Let x represent the smaller integer. Then x+1 is the larger. The problem statement tells us

... 2 × larger = -15 + 3 × smaller

... 2(x+1) = -15 + 3x . . . substitute variable expressions for 'larger' and 'smaller'

... 2x +2 = 3x -15 . . . . . eliminate parentheses

... 17 = x . . . . . . . . . . . . .add 15-2x

The smaller integer is 17, so the larger is 18.

_____

Check

2×18 = 36 = 3×17 -15 = 51-15