Question

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

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

Answer 2

Given:-

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

To find:-

The integer.

Assumption:-

Let the three consecutive integers be x, (x + 1) and (x + 2)

Solution:-

ATQ,

3 times the smallest integer is 14 more than the largest integer.

Hence,

$\sf{3\times x = (x + 2)+14}$

= $\sf{3x = x + 2+14}$

Taking variables on the LHS and the constants on the RHS

= $\sf{3x - x = 16}$

= $\sf{2x = 16}$

= $\sf{x = \dfrac{16}{2}}$

= $\sf{x = 8}$

Therefore,

1st number = x = 8

2nd number = x + 1 = 8 + 1 = 9

3rd number = x + 2 = 8 + 2 = 10

Verification:-

3 times the smallest integer must be 14 more than the largest integer.

Hence,

3x = x + 2 + 14

= $\sf{3\times 8 = 8 + 2 + 14}$

= $\sf{24 = 10 + 14}$

= $\sf{24 = 24}$

Hence,

LHS = RHS [Verified]

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