Help with a math problem.?

Question

Thanks to anyone who can help.

Suppose you have two numbers. The difference of the two numbers is 12. The product of the two numbers is 17. Multiply the larger of the two numbers by 100, add 50 times the smaller number to that, round the total to the nearest whole number, and that is the answer.

Answer 1

This was a long problem but I got the answer. The answer is either -792 or 1392. I'm going to post the answer first then in my edit I'll explain how I did it.


--edit
How I did it.. okay so let's translate first
Difference of two numbers is 12 ==> x - y = 12
Product of the two numbers is 17 ==> xy = 17

Okay let's focus on those two for now...

first I would separate the x on the first equation so it'll be <> x = 12+y
Then I'd substitute that x in for the second equation so <> xy = 17 ==> y(12 + y) = 17
distribute and move the 17 over <> 12y + y^2 - 17 = 0
Now use the quadratic formula. Here's a link to the formula:
http://www.purplemath.com/modules/quads/qform01.gif

so then the y^2 +12y - 17 = 0 would translate to a =1, b=12 and c=-17
Plug that in (I tried to type up the formula with the numbers in it but it turned out too messy and hard to read... but if you really need it add more info to your question and I'll get back to you).
You should get two answers
when you use plus ==> 1.280109889
when you use minus => -13.28010989
...
That's only part of the story. Now you know that those two numbers equal y. So then you substitute that back into the second equation so you get x(1.280109889) =17.
Divide 17 by 1.280109889 to get x.
x should be 13.28010989

Next do the same thing for the other y you got. so you get x(-13.28010989) =17.
Divide 17 by -13.28010989 to get x
x should be -1.280109889

So now you have two sets of x,y coordinates they should be
(-13.28010989, -1.280109889)
and
(1.280109889,13.28010989)

Finally the last step:
"Multiply the larger of the two numbers by 100, add 50 times the smaller number to that, round the total to the nearest whole number, and that is the answer."
that basically means 100(big number) + (50 small number) = answer

So for the first set of things we get 100(-1.280109889) + 50(-13.28010989) = answer
Keep in mind the negative 13 is smaller because it's more negative. So the answer should be "-792.0164834" Rounded = -792
Then do the same for the other set of coordinates so it'll be: 100(13.28010989) + 50(1.280109889) = answer
answer = 1392.016483 or rounded = "1392"

... phew

so the two answers are -792 and 1392

that took a long time for me to do and write out; so please pick me as best answer.

--edit x2
Keep in mind you said "Multiply the larger of the two numbers by..." that does not mean you rule out the negatives. the larger of the two numbers means the larger number (either x or y) of one set. Then you have to consider the other set which also has a "larger of the two numbers" in that set. So thus you get two answers

Answer 2

let x be the large #
let y be the small #

x - y = 12
x*y = 17

x-y=12
x=12+y
sub that in for x in the second problem

xy=17
(12+y)y=17
12y + y^2 = 17
y^2 + 12y = 17
y^2 + 12y - 17=0

quad formula
a = 1; b=12; c=-17
(-b +or- sqr(b^2-4ac))/2a
(-(12) + or - sqrt((-12)^2 - 4(1(-17))/2(1)
(-12 + or - sqrt(144+68))/2
(-12 + or - sqrt(212))/2

rounded to the nearest hundred

-12/2 + 14.56/2 and
-12/2 - 14.56/2

-6 + 7.28 and
-6 - 7.28

-1.28 and -13.28

that is the y value
-13.28 works

now x - y = 12
x - (-13.28) = 12
x + 13.28 = 12
x = 12 - 13.28
x = -1.28
(-1.28 * -13.28 = 16.9984 ... cause sqr(212) is irrational and our answer is an approximation)

100 * (-1.28) + 50 * (-13.28) =
-128 - 664 = -792

-792 is your answer

Answer 3

x-y=12---(1)
xy=17---(2)
from equation (1),
x=12+y---(3)
replace equation (3) to equation (2):
(12+y)y=17
12y+y^2=17
y^2+12y-17=0
y=1.28,-13.28
after getting the value of y,replace it on either equation(1)/(3) or (2):
x=13.28,-1.28
1st answer:x=13.28,y=1.28
2nd answer:x=-1.28,y=-13.28
since there are 2 sets of answers,i choose the 1st set of answer since you stated that we need to multiply the larger of the 2 numbers.
if so,
(13.28x100)+(1.28x50)=1392.
the answer i found is 1392.1392 is a whole number.so i hope it's correct. =)

Answer 4

let the numbers be x and y{x>y}
x-y=12----------------------1
xy=17
now,let's find x+y
(x+y)^2=(x-y)^2-4xy
(x+y)^2=144-68
(x+y)^2=76
x+y=8.7177----------------2
add 1 and 2
2x=20.7177
x=10.35885
y=-1.64115

to find 100x+50y
=50x+50y+50x
=50(x+y)+50(10.35885)
= 50(8.7177)+517.9425
=435.885+517.9425
=953.8275

the nearest whole number is 954.