If the first and third of three consecutive odd integers are added, the result is 69 less than five times the second integer. Find all three integers.
first represent the unknowns with variables:
let x = first number
let x+2 = second number
let x+4 = third number
*since they are consecutive, and all of them are odd, they have a difference of 2, that's why it's x, x+2, x+4*
now, setup equation using the given conditions:
x + x+4 = 5(x+2) - 69
distribute the 5 (right side of equation) and then combine similar terms,
2x + 4 = 5x + 10 - 69
2x + 4 = 5x - 59
simplify this and solve for x.
hope this helps. :)
thank you
5+16x<-59
To solve this problem, we'll need to set up equations based on the given information and then solve for the three consecutive odd integers.
Let's assume the three consecutive odd integers are represented by n, n+2, and n+4.
According to the problem, "the first and third of three consecutive odd integers are added, the result is 69 less than five times the second integer." This can be expressed as:
(n) + (n+4) = 5(n+2) - 69
Simplifying the equation, we get:
2n + 4 = 5n + 10 - 69
Now solve for n:
2n + 4 = 5n - 59
Subtract 2n from both sides:
4 = 3n - 59
Add 59 to both sides:
63 = 3n
Divide both sides by 3:
n = 21
Therefore, the three consecutive odd integers are 21, 23, and 25.
To check if these numbers satisfy the given condition, substitute them back into the equation:
21 + 25 = 5(23) - 69
46 = 115 - 69
46 = 46
Since the equation holds true, the solution is valid. Therefore, the three consecutive odd integers are 21, 23, and 25.