Question

What are two consecutive integers, such that five times the smaller minus three times the larger is 51? What is the smallest integer?

Answer 1

Answer:   27

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Work Shown:

x = smaller integer

x+1 = larger integer

x and x+1 are consecutive integers since the larger follows right after the smaller

5*(smaller) - 3*(larger) = 51

5*(x) - 3*(x+1) = 51

5x - 3x - 3 = 51

2x - 3 = 51

2x = 51+3

2x = 54

x = 54/2

x = 27

x+1 = 27+1 = 28

The two consecutive integers are 27 and 28.

Answer 2

Let us consider two integers to be x and x+1:

x = smaller integer

x+1 = larger integer

Given: x and x+1 are consecutive integers.

$5*(smaller) - 3*(larger) = 51\\\\5*(x) - 3*(x+1) = 51\\\\5x - 3x - 3 = 51\\\\2x - 3 = 51\\\\2x = 51+3\\\\2x = 54\\\\x = 54/2\\\\x = 27$

The value of x i.e. smaller integer comes out to be 27

Thus, x+1 = 27+1 = 28

Therefore, the two consecutive integers are 27 and 28.

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