SOLUTION: The difference between two positive numbers is 3 and the product between these two numbers is 28. Set-up two equations and solve to find the two numbers.

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Question 389894: The difference between two positive numbers is 3 and the product between these two numbers is 28. Set-up two
equations and solve to find the two numbers.
Found 2 solutions by ewatrrr, MathLover1:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi, 

  The difference between two positive numbers is 3     

Let x and (x+3) represent the two positive numbers

Question states***

 x(x+3) = 28

  x^2 + 3x - 28 = 0

factoring

 (x -7)(x-4)= 0

 (x +7= 0

    x = -7  Tossing out negative solution

  (x-4)= 0

     x = 4  the two positive numbers  are 4 and  7 (4+3)



CHECKING Our Answer

 4*7 = 28

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let a numbers be a and b, and let a%3Eb
The difference between them is 3+

a+-+b+=+3..........(1)
and the product between these two numbers is 28
a%2Ab+=+28...........(2)
solve the system:
a+-+b+=+3..........(1)..solve for a and substitute in (2)
a%2Ab+=+28...........(2)
---------------------------------
a+=+3+%2B+b..........(1)
%283+%2B+b%29%2Ab+=+28...........(2)
3b+%2B+b%5E2+=+28
b%5E2+%2B+3b+-28+=0......solve for b

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2B3%2Ax-28=0 ( notice a=1, b=3, and c=-28)





x+=+%28-3+%2B-+sqrt%28+%283%29%5E2-4%2A1%2A-28+%29%29%2F%282%2A1%29 Plug in a=1, b=3, and c=-28




x+=+%28-3+%2B-+sqrt%28+9-4%2A1%2A-28+%29%29%2F%282%2A1%29 Square 3 to get 9




x+=+%28-3+%2B-+sqrt%28+9%2B112+%29%29%2F%282%2A1%29 Multiply -4%2A-28%2A1 to get 112




x+=+%28-3+%2B-+sqrt%28+121+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-3+%2B-+11%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-3+%2B-+11%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-3+%2B+11%29%2F2 or x+=+%28-3+-+11%29%2F2


Lets look at the first part:


x=%28-3+%2B+11%29%2F2


x=8%2F2 Add the terms in the numerator

x=4 Divide


So one answer is

x=4




Now lets look at the second part:


x=%28-3+-+11%29%2F2


x=-14%2F2 Subtract the terms in the numerator

x=-7 Divide


So another answer is

x=-7


So our solutions are:

x=4 or x=-7



since your numbers are positive, you will take only x=b=4
to find a
a+-+b+=+3...plug in b=4

a+-+4+=+3

a+=++3+%2B+4

a+=+7

so, your numbers are :a+=+7 and b=4