Question

Please help!!!! I've been stuck for hours!!!!
The product of three consecutive whole numbers is 990. What is the sum of the three whole numbers?
A.30
B.33
C.63
D.96

Answer 1

I got that but I have to explain it mathematically, and I have the equation I just don't know how to solve it.
Equation: (X)*(X+1)*(X+2)=990

Answer 2

Can you multiply the left side?

Answer 3

(x - 1) (x) (x + 1) = 990
x = 10
9+10+11 = 30

Answer 4

My main question is how would you solve the equation (if the one I got is correct) because I'm not sure how.

Answer 5

You first need to multiply out the left side.
Then you need to try to factor it.

Answer 6

another approach would be to use logic as follows: the numbers that end in 0 must have 10 as a factor, so you only have 3 possibilities. Not an analytic approach, I know, but perhaps a time-saver

Answer 7

I get what you mean but I have to explain it mathematically and my teacher prefers it in step (or similar to steps) so your way doesn't exactly work. But it really is a good way thank you!

Answer 8

What class is this?

Answer 9

Refer to the attachment from Mathematica 9.

Answer 10

considering he wants they want a 'mathematical explanation' and mine didn't meet the criteria, i doubt a mathematica graph is what their teacher wants

Answer 11

he/she wants*

Answer 12

9+10+11=3*10=30

Answer 13

I was going to say if this is a calculus course or later we could use newton's method to find the root to the equation.

Answer 14

Well you have to be able to explain that
x, x+1 and x+2 represent the three consecutive numbers
then write down the equation you got to multiply
write down next to it: solve the equation to find x, because when I have x, I can use it in the summation formula: x+x+1+x+2
Plug it in and calculate the sum. That's a proper explanation to indicate you know the different steps you have to perform.

Answer 15

@Kainui This is for an 8th grade math class (not specified what kind of math sorry)

Answer 16

they can't expect you to solve a cubic like this for 8th grade math...

Answer 17

I think this really just relies on knowing a method for factoring a cubic.

See, when you multiply it out, you are simply finding a single root of a whole number. It's really not that bad or uncommon.

Answer 18

I know, we didn't learn it this year maybe we have to because it's AP

Answer 19

I honestly wouldn't know how to factor x^3+3x^2+2x-990=0

Answer 20

If any of my HS pupils was ever to explain the solving steps of such a system problem as I wrote down I'd ace them, without discussion.

Answer 21

I believe the second method shown on this site shows the reasoning of how to factor this. I haven't worked it out yet, but it seems to be right.

http://www.wikihow.com/Factor-a-Cubic-Polynomial

Answer 22

@TMussetti, are you seeing 'linear equation systems' in class right now?

Answer 23

Nope, that's what we're learning when we're come back from break

Answer 24

Yeah, use the method on that site where you use the "free term" to figure it out. You might seem overwhelmed at first because there are about 24 divisors of 990 but you can reason out that it won't be one of the larger ones with another easy little trick.

In fact, you know it has to be almost cube root of 990 since we're looking for a number that is almost cubed to make 990.

Answer 25

Actually I've ran into a lot of these consecutive number things, but it never really dawned on me until just now to consider writing them out as being the middle number with plus and minus for the other consecutive numbers instead of just purely positive. Then you know that the nth root of their product is a good first guess.

Answer 26

Yeah, I understand it a bit better now thanks @Kainui. If I end up totally understanding I'll be slightly ahead of my class :D

Answer 27

let the numbers =x, x+1, x+2
sum = 30 3 x + 3 = 30 solve for x gives x = 9
x + 1 = 10, x + 2 = 11
9*10*11 = 990

Answer 28

Thank you so much!!! I love how you took a whole other approach. @triciaal Genius!!!!!!!!!!!!!!

Answer 29

but we aren't told that they sum to 30.....

Answer 30

you could trial and error each option, i guess, but i prefer thinking that 10 must be a factor and working from there

Answer 31

It's one of the choices though

Answer 32

high school level
multiple choice
first one worked

Answer 33

If you weren't given answer choices your method would completely fall on its face @triciaal

Answer 34

it's a tactic that works, but I wouldn't give a student good marks for that approach to the problem

Answer 35

Well like you said @TuringTest these are cubic equations (sorry if I'm wrong) and that it's weird that they're giving me this, so a simple method to get the answer wouldn't be bad for this.

Answer 36

right, just that you rejected my method of starting with stating that 10 must be a factor because it wasn't 'mathematical' enough of an explanation, but working backwards from multiple choices is a far worse way to approach to problem, since at least with my way you get the answer without needing the choices. Just think about which method is better from a mathematical understanding perspective.

Answer 37

Well, I didn't reject it right away I tried to apply it on another sheet to see how I'd do it but your explanation it's self wasn't the best for me. But then again math isn't my strong point. You could have been 100% right and I just didn't understand it.

Answer 38

fair enough :) I thinnk @Kainui has found the only right analytical approach

Answer 39

Agreed