Question

The smallest of three consecutive integers is added to four times the largest integer;
the result so obtained is 15 less than three times the middle integer. Find the integers.​

Answer 1

Answer:

-10,-9,-8

Step-by-step explanation:

Given :-

The smallest of three consecutive integers is added to four times the largest integer;

the result so obtained is 15 less than three times the middle integer.

To find:-

Find the Integers ?

Solution :-

Let the consecutive three integers be X,X+1,X+2

The smallest integer be X

The Middle integer = X+1

The Largest integer = X+2

4 times the largest integer

= 4(X+2)

= 4X+8

Now

The sum of the smallest integer and 4 times the largest integer

= Smallest integer + 4× Largest integer

= X+4X+8

= 5X+8 ---------(1)

and Three times the middle integer

= 3(X+1)

= 3X+3

15 less than the three times the middle integer

= 3X+3 -15

= 3X-12 ----------(2)

According to the given problem

The smallest of three consecutive integers is added to four times the largest integer;

the result so obtained is 15 less than three times the middle integer.

=> Smallest integer + 4× Largest integer

= 3× middle integer -15

(1) = (2)

=> 5X+8 = 3X-12

=> 5X-3X = -12-8

=> 2X = -20

=> X = -20/2

=> X = -10

The smallest integer (X) = -10

The middle integer ( X+1 ) = -10+1 = -9

The largest integer (X+2) = -10+2 = -8

Answer:-

The required three consecutive integers are -10,-9,-8

Check:-

The three consecutive integers = -10,-9,-8

The sum of the smallest integer and 4 times the largest integer

= (-10)+4(-8)

= -10-32

= -42 -------(1)

15 less than the three times the middle integer

= 3(-9) -15

= -27 -15

= -42 -------(2)

From (1) &(2)

The sum of the smallest integer and 4 times the largest integer = 15 less than the three times the middle integer

Verified the given relations in the given problem.