1. If the first and third of three consecutive odd integers are added, the result is 51 less than five times the second integer. Find the third integer.
Let the 3 numbers be x, (x + 1) and (x + 2).
Then, x + (x + 2) = 5(x + 1) - 51
Solve for x.
We want "three consecutive odd integers". These look like
2k+1, 2k+3, and 2k+5
We're told
2k+1 + 2k+5 = 5*(2k+3) - 51 so
4k+6 = 10k + 15 - 51 or after rearranging
42 = 6k and k=7 so the numbers are
15,17 and 19
Test:
15 + 19 = 5*17 -51 or
34 = 85 - 51
Well, I guess I won't be clowning around with this one. The third integer is 19.
To find the third integer, let's solve the equation:
x + (x + 2) = 5(x + 1) - 51
First, distribute 5 to x + 1:
x + (x + 2) = 5x + 5 - 51
Simplify:
2x + 2 = 5x - 46
Subtract 2x from both sides:
2 = 3x - 46
Add 46 to both sides:
48 = 3x
Divide both sides by 3:
x = 16
Now that we have the value of x, we can find the third integer by substituting it into the equation:
Third integer = x + 2 = 16 + 2 = 18
Therefore, the third odd integer is 18.
To solve this problem, we are given that the first and third of three consecutive odd integers, let's call them x, (x + 1), and (x + 2), are added together. We are also given that the result is 51 less than five times the second integer.
So, we can set up an equation: x + (x + 2) = 5(x + 1) - 51.
To simplify, we can combine like terms: 2x + 2 = 5x + 5 - 51.
Now, let's simplify further by combining like terms: 2x + 2 = 5x - 46.
Next, let's isolate the variable by subtracting 2x from both sides: 2 = 3x - 46.
We can now add 46 to both sides: 48 = 3x.
Finally, divide both sides by 3 to solve for x: x = 16.
So, the third integer would be x + 2 = 16 + 2 = 18.
Therefore, the third integer is 18.
X+x+2=5x+5-15
2x+2=5x-10
2+10=5x-2x
12=3x
3x/3=12/3
X=4.