algebra help please?!!!?

Question

Three consecutive integers have the sum of 153.
What is the first integer?

Five times the first of three consecutive even integers is fourteen more than three times the second.
What is the third integer?

Thanks!

Answer 1

n + (n + 1) + (n + 2) = 153

3n + 3 = 153

3n = 150

n = 50

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5 * n = 3 * (n + 2) + 14

5n = 3n + 20

2n = 20

n = 10

The third integer is 14.

Answer 2

Three consecutive integers are: n, n+1 and n+2

Their sum is 153:
n + (n + 1) + (n + 2) = 153

3n + 3 = 153 // -3

3n = 150 // divide by 3

n = 50

50, 51 and 52 are 3 integers and their sum is 153.

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Three consecutive even integers are n, n+2 and n+4

Five times the first is 5n
Three times the second is 3(n + 2)

5n - 14 = 3(n + 2)

5n - 14 = 3n + 6 // - 3n

2n - 14 = 6 // + 14

2n = 20

n = 10
The third integer is n + 4 = 14

5n = 5 * 10

5n - 14 = 50 - 14 = 36 = 3 * 12 = 3(n + 2)

Answer 3

x + (x+1) + (x + 2) = 153
3 x + 3 = 153
3 x = 150
x = 50



5x = 14 + 3(x+2)
2x = 20
x = 10
x + 2 = 12 (second integer)
x + 4 = 14 (third integer)

You need to understand how I came up with these or you will not pass the test.

Answer 4

1) The first integer is 17
2) The third integer is 54

Answer 5

Lets figure out what we know

Lets say that the least interger is x
So the next interger is x+1, becasue it is one more
And the last interger is x+2, because it is two more

So (x)+(x+1)+(x+2)=153

3x+3=153

Subtract 3 from each side

3x=150

Divide each side by 3

x=50

The 1st Number is 50, 2nd is 52, 3rd 53

Problem Number 2

Lets say that the least interger is x
So the next interger is x+2, becasue the next EVEN Number is 2 more
And the last interger is x+4, because The next even number is 4 more

Distribute
5x=3(x+2)+14

Combine like terms
5x=3x+6+14

Subtract 3x from each side
5x=3x+20

Divide each side by 2
2x=20

so x is equal to 10
x=10

the first number is 10, so the next even number is 12 and the last even number is 14

So answers....

Problem 1: 50
Problem 2: 14

Answer 6

set up the equation
x+(x+1)+(x+2)=153
3x+3=153
3x=150
x=50
so first integer is 50 then 51, 52

2nd part doesnt make sense b/c if they were even then they cant be consucetive.

Answer 7

For increasing cubic binomials the final formulation is as follows: (a + b) ^ 3 = a^3 + 3*a^2*b^a million + 3*a^a million*b^2 + b^3 on your case, a is x and b is -y^5 So (x - y^5)^3 = x^3 + 3*x^2*(-y^5)^a million + 3*x^a million*(-y^5)^2 + (-y^5)^3 Simplified: =x^3 - 3x^2*y^5 + 3x*y^10 - y^15 :D

Answer 8

n+(n+1)+(n+2)=153
3n+3=153
3n=150
n=150/3
n=50