Answer:
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
