Math Question...?

Question

Ok i have a question on my math homework
It says

"The sum of three consecutive even
integers is less than 84. What are the greatest possible value of these integers?"

To begin with i dont understand how to find those numbers all i know its something like
( ) + ( ) + ( ) < 84

Please help me understand these problems
Thank You.

Answer 1

okay. less than 84 means <84

then, 3 consecutive even integers. let's take 2. if x=2, then the three even consecutive numbers would be 2, 4, and 6. Hence, x, x+2, and x+4. Got it?

Now, there sums are less than 84. th eequation is (x)+(x+2)+(x+4)<84 or simplifiied, would be 3x+6<84.

Subtract 6 on both sides.
3x<78

divide by 3.
x<26

x is any even number less that 26.

Check: if x is 24:
24+26+28= 78

Get it?

Answer 2

You have three consecutive even integers. Let the first integer be n, then the three integers are n, n+2, and n+4. Thus you have n+n+2+n+4<84. You can then solve this equation for n:

n+n+2+n+4<84
3n+6<84
3n<78
n<26

Since this inequality is strict, and since n is an even integer, this means the highest value n can have is 24 (it would be 26 if we replaced < with ≤). Thus your integers are no greater than 24, 26, and 28, respectively.

Answer 3

Well, first of all, you can set variables for this type of problem. Setting variables is a great habit that you can use when you are doing calculus, trig, and even comp. science. So, set three variables, x, y, and z. Then, think about the different possibilities of the values. You know that one value cannot be 84, since they all have to be the largest. So, the only way that you can do this problem is by dividing 84 by 3 (28), and using that value to determine your actual total. Since it wants a value less of 84, the values should be 28, 29, and 26, the biggest numbers possible in this problem.

Answer 4

(n) + (n+2)+ (n+4) < 84

Answer 5

well since they are consecutive even you can represent them like this:
x=smallest number
x+2= middle
x+4= highest

then it is
x+x+2+x+4 <84
3x+6<84
3x <78
x < 26

Answer 6

Try

(x)+(x+2)+(x+4) <= 84

solve for x, you answer will be (x, x+2, x+4)