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in Linear Equations by (15.2k points)

Find all pairs of consecutive even positive integers both of which are larger than 8 such that their sum is less than 25.

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1 Answer

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by (15.7k points)

Let the pair of consecutive even positive integers be x and x + 2. 

So, it is given that both the integers are greater than 8 

Therefore, 

x > 8 and x + 2 > 8

When, 

x + 2 > 8 

Subtracting 2 from both the sides in above equation 

x + 2 – 2 > 8 – 2 

x > 6 

Since x > 8 and x > 6 

Therefore, 

x > 8 

It is also given that sum of both the integers is less than 25 

Therefore, 

x + (x + 2) < 25 

x + x + 2 < 25 

2x + 2 < 25 

Subtracting 2 from both the sides in above equation 

2x + 2 – 2 < 25 – 2 

2x < 23 

Dividing both the sides by 2 in above equation

\(\frac{2{\text{x}}}{2}< \frac{23}{2}\)

x < 11.5 

Since x > 8 and x < 11.5 

So, the only possible value of x can be 10 

Therefore, x + 2 = 10 + 2 = 12 

Thus, the required possible pair is (10, 12).

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