SOLUTION: 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

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Question 75454: 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 thats the answer.
Found 2 solutions by checkley75, ptaylor:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
X-Y=12, X=Y+12
XY=17
(Y+12)Y=17
Y^2+12Y-17=0
USING THE QUADRATIC EQUATION WE GET:
X=(-12+-SQRT[-12^2-4*1*-17])/2*1
X=(-12+-SQRT[144+68])/2
X=(-12+-SQRT212)/2
X=(-12+-14.56)/2
X=(-12+14.56)/2
X=2.56/2
X=1.28 ANSWER.
X=(-12-14.56)/2
X=-26.56/2
X=-13.28 ANSWER.
1.28*100+(-13.28*50)
128-662.5
-535 FINAL ANSWER.

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=larger number
And y=smaller number
Now we are told that:
x-y=12----------------------------------eq 1
and
x%2Ay=17-----------------eq 2
We can see from a quick inspection that these two numbers are not going to be whole numbers
From eq 2, y=17%2Fx. Substitute this value into eq 1 and we get:
x-17%2Fx=12 multiply each term by x
x%5E2-17=12x subtract 12x from both sides
x%5E2-12x-17=0 we will solve using the quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%2812+%2B-+sqrt%28+144%2B68+%29%29%2F%282%29+
x+=+%2812+%2B-+sqrt%28+212+%29%29%2F%282%29+
x+=+%2812+%2B-+14.5602%29%2F%282%29+
x+=+%2812+%2B14.5602%29%2F%282%29+
x+=+%2826.5602%29%2F%282%29+
x=13.2801----------------------------larger number
We'll forget about the negative value for x because the positive value works
ON SECOND THOUGHT, WE NEED TO LOOK AT THE NEGATIVE VALUE FOR X BECAUSE THIS SOLUTION WILL YIELD A DIFFERENT ANSWER. SEE BELOW:
substitute x=13.2801 into eq 1 and we get:
13.2801-y=12 subtract 13.2801 from both sides
-y=-1.2801 multiply both sides by -1
y=1.2801---------------------------------smaller number
CK
%2813.2801%29%281.2801%29=17
17=17 close enough
and
13.2801-1.2801=12
12=12
Multiply the larger number by 100 and we get
%2813.2801%29%28100%29=1328.01
50 times the smaller number is:
%2850%29%281.2801%29=64.005
Now add these two numbers together and round to the nearest whole number:
1328.01%2B64.005=1392.015
Rounded to the nearest whole number we have
1392---------------------------------------------------answer!!! if I didn't make a mistake
NOW WE WILL LOOK AT THE NEGATIVE VALUE FOR X:

x+=+%2812+-+14.5602%29%2F%282%29+
x+=+%2812+-+14.5602%29%2F%282%29+
x=-2.5602%2F2=-1.2801--------------------------larger number
Substitute x=-1.2801 into eq 1:
-1.2801-y=12 add 1.2801 to both sides
-y=12%2B1.2801=13.2801 multiply both sides by -1
y=-13.2801-------------------------------------------smaller number
So now we have:
%28100%29%28-1.2801%29%2B%2850%29%28-13.2801%29 which equals
-128.01-664.005=-792.015 or
-792------------------------another answer

Hope this helps----ptaylor