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

The third integer is 25

Step-by-step 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