SOLUTION: can you please answer this problem? Joey is 9 years older than Marivic. Six years ago, the product of their ages is 190. Find their present ages. I hope to hear you soon. thank y

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: can you please answer this problem? Joey is 9 years older than Marivic. Six years ago, the product of their ages is 190. Find their present ages. I hope to hear you soon. thank y      Log On


   



Question 584725: can you please answer this problem? Joey is 9 years older than Marivic. Six years ago, the product of their ages is 190. Find their present ages.
I hope to hear you soon. thank you!

Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
im using first letter of names as variables
J=highlight%289%2BM%29 (Joey is 9 years older than Marivic)
%28J-6%29%28M-6%29=190 (Six years ago, the product of their ages is 190)
%28highlight%289%2BM%29-6%29%28M-6%29=190
%28M%2B3%29%28M-6%29=190
%28M%5E2-3M-18%29=190
M%5E2-3M-208=0solve for M and M has to be positive because its an age
fastest way is to find two numbers that multiply to get -208 and add to get -3
what i do is take two of the same number and multiply them to see if its close to 208
i started with 15*15=225 the 14*14=196 this tells me that the two numbers are close and i know they are three away from each other
i try 14*17=238 then 13*16=208, got the right number but its positive so one the numbers has to be negative, since there was a -3 difference the larger number has to be negative, -16*13=-208 and -16+13=-3
now that sounds like a lot of work but I did all of that in 10 secs in my head and a calculator.
%28M-16%29%28M%2B13%29=0numbers from above put into problem and now set equal to 0 and solve, only the possitive answer is needed
M=16
J=9%2B16
J=25