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

Question

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

0

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.

the two integers are 17 and 18

Step-by-step 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.

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Check

2×18 = 36 = 3×17 -15 = 51-15