byron is 3 years older than doug.the product of their ages is 40.how old is doug

Question

Integrated algebra 

Answer 1

Hi, Sani! We should set this up as an algebra problem with one variable - let's use x.

 

Doug is x years old, so Byron is x+3 years old. The product of their ages would then be x times x+3:

x(x+3) = 40

x² + 3x = 40

x² + 3x + 40 = 0

 

Now, factor the equation:

(x+8)(x-5) = 0

 

Then, solve for both values of x:

x+8 = 0

x = -8

 

x-5 = 0

x = 5

 

As no one can have a negative age, we simply disregard x=-8 as invalid. Therefore, Doug is 5 years old & Byron must be 5+3 - or 8 years old.