Question

find three consecutive even integers so that the twice the sum of the second and third is twelve less that six times the first

a. 9, 10, 11
b. 6, 8, 10
c. 2, 4, 6
d. 3, 4, 5
e. none of the above

Answer 1

@bibby

Answer 2

3 consecutive even integers (consecutive evens are split by factors of 2)
x, x+2, x+4

Automatically we can cross out a and d

Answer 3

now translate the words into an equation
twice the sum of the second and third is twelve less that six times the first

Answer 4

that's the part i was having trouble with, my mind is not grasping translating this problem. which is basically, the entirety of the problem.

Answer 5

let the three integers be x,y and z so y=x+1 and z=x+2

Answer 6

ok, well I'll help you understand the idea before moving on.
Consecutive means one after another. Even means divisible by 2.

so 2,4,6 or 6,8,10 or 4,6,8

now we want to represent this relationship using a variable

x = 2
then y and z would be 4 and 6
or x+2 and x+4 respectively

Answer 7

so according to the problem 2(y+z) = 6x -12

Answer 8

@alekos "consecutive even integers"

Answer 9

that's fine. then y=x+2 and z=x+4 so just substitute y & z into the equation and solve for x

Answer 10

alright, that's starting to make a little more sense. this problem i have no idea even where to begin so you explaining it is helping a ton

Answer 11

well the equation has been written out soooo

Answer 12

i know i'm solving it now

Answer 13

oh yeah that wasn't meant to sound impatient

Answer 14

i'm getting B. 6, 8, 10

Answer 15

that's not what I got

Answer 16

2(y+z) = 6x -12
y=x+2
z=x+4
2(x+2+x+4)=6x-12
2(x+6)=6x-12
2x+12=6x-12 subtract 2x and add 12
24=4x
x=6

Answer 17

5th line should be 2(2x+6) = 6x-12

Answer 18

yeah it should be 12,14,16 my bad