SOLUTION: On the word problems using multiplication is throwing me off, such as this problem "Find two numbers whose sum os 24 and whose product is 143"

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Question 170611: On the word problems using multiplication is throwing me off, such as this problem "Find two numbers whose sum os 24 and whose product is 143"
Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
lets call the 2 numbers a and b
:
sum of the numbers is a+b which equals 24----------------->a+b=24...eq 1
:
the product of the numbers is ab which equals 143.-------->ab=143...eq 2
:
lets take eq 1 and write it in terms of a--->a=24-b
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take a's value from eq 1 and plug it into eq 2
:
(24-b)b=143---distribute--->
:

so b can be 11 or 13 if b is 11 then a is 13 if b is 13 the a is 11
:our two numbers are

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=4 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 13, 11. Here's your graph:

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