Question

Translate this problem to an equation and solve.
The product of 2 positive consecutive even integers is 48.
What is the smaller number

Answer 1

Let n be the smaller integer. What will be the other one?

Answer 2

n+2?

Answer 3

n+1 is the next integer.

Answer 4

oh ok

Answer 5

n+2 would be the next odd/even integer but they don't ask about that.

Answer 6

n(n+1)=48

Answer 7

Yeah, that last one. Because they said it's the product of those. Therefore you must use multiplication.

Answer 8

what do i do next?

Answer 9

2n+1=48?

Answer 10

No

Answer 11

n(n+1) = 48

Answer 12

n^2+1=48?

Answer 13

\[\implies n^2 + n =48\]

Answer 14

2n^2=48?

Answer 15

no.

Answer 16

You can't combine an n and an n^2 term

Answer 17

oh ok

Answer 18

\[\implies n^2 + n - 48 = 0\]

Then use the quadratic formula.

Answer 19

whats tht?

Answer 20

Although this makes no sense since there are no integer solutions to this equation.

Answer 21

oh crap sorry

Answer 22

They did say 'even' integers.

Answer 23

So it's
n(n+2) = 48

Answer 24

oh hahaha

Answer 25

\[\implies n^2 + 2n = 48\]\[\implies n^2 + 2n - 48 = 0\]

Answer 26

2n+2=48
-2 -2
2n+46
/2 /2

Answer 27

Then you can factor that?

Answer 28

no. You keep adding when you need to multiply.

Answer 29

Ugh what

Answer 30

n(n+2) = n(n) + n(2)

Answer 31

= n^2 + 2n

Answer 32

Do you use twiddla at all?

Answer 33

twiddla?

Answer 34

http://www.twiddla.com/591991

Answer 35

it's a whiteboard so I can demonstrate better.

Answer 36

oh oksure?

Answer 37

hello

Answer 38

Hi

Answer 39

So

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

Answer 40

yes

Answer 41

So can you factor that from there?

Answer 42

factor?

Answer 43

Like
(n+a)(n+b)

Where a + b = 2
And a*b = -48

Answer 44

i dont understand

Answer 45

Factoring. Or solving quadratic equations

Answer 46

Have you done this before?

Answer 47

no?

Answer 48

Hrm. Well I guess you can solve this using some level of intuition.

Answer 49

What two even numbers can you multiply to get 48 that are separated by a distance of 2?

Answer 50

8 and 6?

Answer 51

Correct. And the smallest of those is?

Answer 52

6. oh my god thank you so much ahaha i apprectiat it

Answer 53

No problem ;)