Math Problem Below Needs Help Solving?

Question

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.

Answer 1

smallest number is 1.280109889

larger number is 13.280109889

13.280109889-1.280109889=12

13.280109889 x 1.280109889=17

larger number multiplied by 100 is 1328.0109889 (calculators show one digit less)

smaller number multiplied by 50 is 64.00549445 (calculators show one digit less)

the two added together is 1392.01648335

so your answer is 1392.

Answer 2

Wolverine has made it easy by sending us on the right track.
Here is a variation on his theme:

Let us say that x is the greater of the two numbers.
"The difference of the two numbers is 12"
Then the other number is (x-12).

"The product of the two numbers is 17"
x(x-12) = 17
x^2 -12x -17 = 0

This is a quadratic equation and should allow you to find x (and x-12).

"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."
100x + 50(x-12) -- then round up

100x + 50x -600
150x - 600
150 (x-4) -- then round up

(of course, if you solve for x at the quadratic, you can do this last part with the real numbers instead of x and x-12)

---

The number I get is divible by 199.

Answer 3

1575

Answer 4

x-y=12...(1)
xy=17.....(2)
find x an y
after that ...it'is easy!
--------------------------------------
x=12-y in (2)
y²+12y-17=0.........(A)
this is an equ of second degree (we look to the hygher power of y in this line witch is 2)
its general form is
ay²+by+c=0
with a=1(because 1*y²=y²),b=12,c=-17
we have to calculate
Δ=(b)²-4(axb)=12²-4(-17*1)=12²+68=212
Squared root of Δ=14.56
Δ is > 0 our equ accepte two solutions

y1=
-b+Sqrt ofΔ
------------------
2a


y2=
-b-Sqrt ofΔ
------------------
2a


y1=2.56/2=1.28
y2=-26.56/2=-13.28

....continu!