SOLUTION: the sum of two numbers is 30. if the larger number is divided by the smaller number the quotient is equal to the smaller number. find the numbers.

Question 699126: the sum of two numbers is 30. if the larger number is divided by the smaller number the quotient is equal to the smaller number. find the numbers.
Answer by Stitch(470) (Show Source): You can put this solution on YOUR website!
Equation 1:
Equation 2:
Solve equation 2 for A by multiplying both sides by B

Now plug B^2 into equation 1 for A
Equation 1:

Subtract 30 from both sides to set the equation equal to zero

Now you can use the quadratic equation

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=121 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5, -6. Here's your graph:

Note that B can equal 5 or -6.
--------------------------------
Plug 5 into equation 1 for B
Equation 1:

Subtract 5 from both sides

Check your answer:
5 + 25 = 30 That checks
25 / 5 = 5 That checks
--------------------------------
Plug -6 into equation 1 for B
Equation 1:

Add 6 to both sides

Check your answer:
-6 + 36 = 30 That checks
36 / -6 = -6 That checks
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So for this problem you have two answers: 5 & 25, or -6 and 36

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