Find four consecutive even numbers which add to 76. Give the numbers smallest to largest

Question

Find four consecutive even numbers which add to 76. Give the numbers smallest to largest

Answer 1

Algebra is the way you should solve a problem like this if you are taking Algebra l or a higher level math course. However, you can solve this problem using simple arithmetic.

Find the average of the numbers.

76/4=19

Each pair of numbers must have an average of 19.

The numbers have to be even and consecutive.

18 and 20 have a mean of 19.

The other numbers both can't be greater than 20 or both less than 18.

Therefore pick the next even number greater than 20 (22) and the previous even number less than 18 (16).

The average of 16 and 22 is 19.

The numbers are 16, 18, 20, and 22.

Again, 76/4=19. 18 and 20 and 16 and 22.

 

Answer 2

The easiest way to do this is to set up an algebraic equation where x is your first number, and each consecutive number adds another 2.

 

x+(x+2)+(x+2+2)+(x+2+2+2)=76

 

x is your first number, (x+2) is your second, (x+2+2) is your third and your fourth is (x+2+2+2)

 

simplify the equation and you get

x+(x+2)+(x+4)+(x+6)=76

simplify it more and you get

4x+12=76

 

Solve for x

 

4x+12-12=76-12

4x=64

4x/4=64/4

x=16

 

plug x=16 into each of your number expressions and you find that your numbers are 16, 18, 20, 22.

 

Simple addition can check this answer for you.

 

16+18+20+22=76

Answer 3

The difference between any 2 even numbers is 2.

You can write 4 consecutive even numbers as n + (n+2) + (n+4) + (n+6)

So, n + (n+2) + (n+4) + (n+6) = 76

or 4n + 12 = 76

or 4n = 64

or n = 64/4 = 16

Thus, your 4 numbers are: 16, 18, 20, 22