Question

Three consecutive integers are such that three times the smallest is 14 more than the largest

Answer 1

Answer:

The three consecutive integers are:

8, 9, 10

Step-by-step explanation:

Given:

There are three consecutive integers.

Three times the smallest is 14 more than the largest.

To find the three integers.

Solution:

Since the integers are consecutive , so each have a common difference of 1.

For example : -3,-2,-1

Let the integers be = $x,(x+1),(x+2)$

Three times the smallest is 14 more than the largest can be given as:

$3x=(x+2)+14$

Simplifying and solving for $x$.

$3x=x+2+14$

$3x=x+16$

Subtracting both sides by $x$

$3x-x=x-x+16$

$2x=16$

Dividing both sides by 2.

$\frac{2x}{2}=\frac{16}{2}$

∴ $x=8$

Smallest integer = 8

Next integer = 9

Largest integer = 10