Question

The product of 2 positive consecutive even integers is 48, what is the smaller number?

Answer 1

Two positive consecutive even integers, than mean 2,4,6,8,10,12....

Even numbers can be algebraically written as 2x, two consecutive, so the second number would be 2x+2

Answer 2

They are even so they have difference of 2:
So, if one number be : x

the other number will be: x + 2

So,
x(x + 2) = 48

\[x^2 + 2x -48 = 0\]

Can you factorize this equation??

Answer 3

Now let's compute an equation:

The sum of those two numbers give 48;
2x+2+2x=48

And solve for x :)

Answer 4

@waterineyes x could be 5, and +2 would be 7 :s

Answer 5

@zepp it is product, not sum

Answer 6

guess and check for this one

Answer 7

I am assuming it as x...

Answer 8

@waterineyes yeah i can, will that give me the answer? And @zepp I'm so confused and this site is annoying me! will you message me and help me?

Answer 9

(2x+2)2x=48 then, thanks satellite :D

Answer 10

@DeaneNicole guess a number and see if it works

Answer 11

Yes you will surely get your answer just factorize that equation..

Answer 12

10 and 12 too big because \(10\times 12=120\) try 6 and 8

Answer 13

@satellite73 I'm trying to PASS my mastery test not fail it!!!

Answer 14

Yeah try 6 and 8..

Answer 15

but that is what you have to do. guess and see what works

Answer 16

@waterineyes I noticed that both methods work :D

Answer 17

there is no other way to do it, pick two consecutive even numbers (wisely) if their product is 48 you win, if not pick bigger or smaller numbers as needed. that is the only way to do this problem

Answer 18

@zepp ., do you know how both method works??

Answer 19

Um, doesn't work :U

Answer 20

if you want to write an equation you can write
\[x(x+2)=48\]
\[x^2+2x=48\]
\[x^2+2x-48=0\] but then you are faced again with the original problem, finding two numbers that multiply to -48 and add to 2
it is the same problem exactly, only now you have an equation and you have made it harder

Answer 21

Do you know or not??

Answer 22

i agree with @satellite73 there is no other method other than guess n checking..
factorizing also u need to guess and put the same effort

Answer 23

Actually it works

(2x+2)(2x)=48
4x^2+4x-48=0

Quadratic: x=3 & -4

2x=2*3=6
2x+2=6+2=8

Answer 24

@ganeshie8 thank you! i have argued this point ad nasueum and keep hearing "but you have to solve an equation" without realizing that solving the equation is identical to solving the original problem

Answer 25

See if you know want this then you can go with quadratic formula,
there is no need of guessing there for factors...

Answer 26

in place of know there will come don't...