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Four consecutive odd integers are such that three times the greatest decreased by the sum of the two smallest results in 37. What is the third integer

User Bitcodr
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1 Answer

4 votes

Answer:

The third integer is 25

Explanation:

* Lets explain how to solve the problem

- Four consecutive odd integers

∵ The difference between each two consecutive odd integers is 2

- Assume that the first odd integer is x

∵ The first odd integer is x

∴ The second odd integer = x + 2

∴ The third odd integer = (x + 2) + 2 = x + 4

∴ The fourth odd integer = (x + 4) + 2 = x + 6

∴ The four odd integers are x , x + 2 , x + 4 , x + 6

- Three times the greatest decreased by the sum of the two

smallest results in 37

The greatest = x + 6

Three times the greatest = 3(x + 6) = 3x + 18

∵ The two smallest are x and x + 2

∴ The sum of the two smallest = x + (x + 2) = 2x + 2

∵ Three times the greatest decreased by the sum of the two

smallest results in 37

(3x + 18) - (2x + 2) = 37

- Multiply the terms of the second bracket by (-)

∴ 3x + 18 - 2x - 2 = 37

- Add the like terms

∴ (3x - 2x) + (18 - 2) = 37

∴ x + 16 = 37

- Subtract 16 from both sides

x = 21

∵ x is the first odd integer

∵ The third odd integer is x + 4

∵ x = 21

- Substitute x by 21

∴ The third odd integer = 21 + 4 = 25

* The third integer is 25

User Zochamx
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