Question

The sum of two numbers is 38 and their product is 165. Find the larger number. PLEASE HELP

Answer 1

First set up the initial equation, x+y = 38
Second equation is x*y =165
x = 38-y
(38-y)y = 165
38y-y^2 =165
-y^2+38y-165
-38+or- square root (38^2-4(-1)(-165))/2(-1)
=5 so y =5 and x = 33

Answer 2

The larger number is 33

Explanation:

Writing and solving a system of equations

Let x and y be the numbers

sum of two numbers is 38

x+y = 38

their product is 165

xy = 165

x = 38-y

Substitute this into xy =165

(38-y) * y = 165

38y - y^2 = 165

-y^2 + 38y -165 = 0

Multiply by -1

y^2 - 38y + 165 =0

Factor

( y-33) ( y-5) = 0

Using the zero product property

y -33 =0 y-5 =0

y =33 y=5

Now we can find x for each solution

x = 38-33 =5 x = 38-5 = 33

The two numbers are 33 and 5

The larger number is 33