Algebra problem. Please help?
Two consecutive odd integers have a product of 483. Find the integers.
What's my first step? How do I find the correct numbers?
Update:The problem says product, not sum. But I don't know the steps to find the answers.
Two consecutive odd integers have a product of 483. Find the integers.
What's my first step? How do I find the correct numbers?
Update:The problem says product, not sum. But I don't know the steps to find the answers.
Comments
Ok, so in math when we don't know numbers we use x to represent them. So we're going to have to set up an equation where we can solve for x. The problem is, there are two numbers but only one equation we can make. But they are consecutive odd integers! For example, 1 and 3. What is the difference between 1 and 3? 2. To turn an odd integer into the consecutive odd integer, you add 2. So the first of out integers will be x. The second integer will be (x+2). That way you can set it up x(x+2)=483. Then solve it
so x will come out to be the lowest integer (for example, 1) and then you will add 2 to find the next integer. For example, 1+2=3. So the integers would be 1 and 3 if x=1.
product is another word for multiply or times. I'll use this * to represent times. Using an x can be confused with a variable in algebra.
First lets consider the even numbers, you know them
2,4,6,8,10....
a formula for even #s is the 'n'-th even number = 2*N
so the 1st even number = 2*1 or 2
so the 2nd even number = 2*2 or 4
so the 3nd even number = 2*3 or 6
and so on.....
and the 18th even number = 2*18 or 36
so what are the odds?
1,3,5,7,9,11......
the are 1 less than the evens
2-1,4-1,6-1,8-1........
so a formula for ODD #s is the 'n'-th odd number = 2*n-1 or 2n-1
there another way of thinking of it
start with 1 and count by 2s which leads to his formula: 1+2(n-1)
but its the same formula. see if you can figure out why.
(multiply it out, rearrange and simplify)
so we are looking for a # 2n-1
the next consecutive odd integer will be 2 more ( like 23 is 2 more than 21)
so the next # is (2n-1) +2 = 2n+1
A. So the two # are 2n-1 and 2n+1
if we multiply them they need to equal 483
(2n-1)(2n+1) = 483
now you need to multiply rearrange and simplify to solve for n
Then plug "n" back into line A above to get your two numbers. 2n-1 and 2n+1
Since the problem asks for integers remember that when you multiply 2 negatives you get a positive.
so there are really 2 solutions the positive pair and the negative pair.
Hope this helps. Good luck.
The answer is 21 and 23.
Just say that you solved it by inspection.
That will drive your math teacher to drink.
Using inspection you ask yourself what number has a square
that is just below your target number, 483.
Well, let's see 20 X 20 +400. That's pretty close.
And the next two odd numbers are 21 and 23. LMAO
Their product (21 X 23) = 483. CORRECT!
Teachers just hate it, when you get an answer by inspection, instead of using a formula!
The square root of 483 is just under 22, so the answer to the question is 21 and 23
oops
my bad
product, not sum
so
(2x+1)(2x+3)=483
4x^2+8x+3=483
4x^2+8x-480=0
x^2+2x-120=0
121=11*11
(x+12)(x-10)
x= -12,10
2x+1= -23,21
so
the numbers are 21 and 23
[also -21 and -23)