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

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) (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) (Show Source): You can put this solution on YOUR website!
Let x=larger number
And y=smaller number
Now we are told that:
----------------------------------eq 1
and
-----------------eq 2
We can see from a quick inspection that these two numbers are not going to be whole numbers
From eq 2, . Substitute this value into eq 1 and we get:
multiply each term by x
subtract 12x from both sides
we will solve using the quadratic formula:

----------------------------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 into eq 1 and we get:
subtract 13.2801 from both sides
multiply both sides by -1
---------------------------------smaller number
CK

close enough
and

Multiply the larger number by 100 and we get

50 times the smaller number is:

Now add these two numbers together and round to the nearest whole number:

Rounded to the nearest whole number we have
---------------------------------------------------answer!!! if I didn't make a mistake
NOW WE WILL LOOK AT THE NEGATIVE VALUE FOR X:

--------------------------larger number
Substitute into eq 1:
add 1.2801 to both sides
multiply both sides by -1
-------------------------------------------smaller number
So now we have:
which equals
or
------------------------another answer

Hope this helps----ptaylor

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