sum of two consecutive even integers is 66. find the two integers

Question

from the book of business maths stats b.com part 1 pg 358

Answer 1

Two integers summing to 66 can be represented by the equation:

 

x + y = 66.

 

X and Y are two consecutive even integers meaning they are divisible by two and right next to each other in the list of even integers. Therefore the larger integer in the list will be two more than the lesser integer in the list.

 

y = x + 2.

 

Plugging into the first equation yields:

 

x + x + 2 = 66 

-> 2x + 2 = 66

->2(x + 1) = 66 [distributive property]

->x + 1 = 33 [divide both sides of equation by 2]

-> x = 32 [subtract both sides by 1]

 

Thus, the two consecutive even integers that add to 66 are 32 and 34.

 

Check: 32 + 34 = 66. 32/2 = 16. 34/2 = 17. 32 and 34 are both even and consecutive.

Answer 2

Hi Eshaal,

The sum of 2 consecutive even integers is 66. This means that if one of the integers is x, the other must be either x-2 or x+2. Therefore, we can write 66=x+(x-2)=2x-2. Solving for x, we find x=34. This means that the other integer is 34-2=32. Indeed, 32+34=66, and we're done!

Hope this helps!

Katie :-)