SOLUTION: 1/5 number of butterflies in agarden are on jasmines and 1/3 of them are on roses.Three times the difference of the butterfllies o jasmines and are on roses are on lillies.If the r

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: 1/5 number of butterflies in agarden are on jasmines and 1/3 of them are on roses.Three times the difference of the butterfllies o jasmines and are on roses are on lillies.If the r      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 626840: 1/5 number of butterflies in agarden are on jasmines and 1/3 of them are on roses.Three times the difference of the butterfllies o jasmines and are on roses are on lillies.If the remaining one is flying frely,then find the total number of butterflies in the garden
Answer by KMST(5398) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the total number of butterflies in the garden.
%281%2F5%29x butterflies are on jasmines.
%281%2F3%29x butterflies (a larger number) are on roses.
The difference is
%281%2F3%29x-%281%2F5%29x=%281%2F3-1%2F5%29x=%285%2F15-3%2F15%29x=%282%2F15%29x
Three times that difference,
3%2A%282%2F15%29x=%282%2F5%29x ,
is the number of butterflies on lilies.
The total number is
x=%281%2F3%29x%2B%281%2F5%29x%2B%282%2F5%29x%2B1 --> x=%281%2F3%2B1%2F5%2B2%2F5%29x%2B1 --> x=%285%2F15%2B3%2F15%2B6%2F15%29x%2B1 --> x=%2814%2F15%29x%2B1
Multiplying both sides of the equal sign times 15:
15x=15%28%2814%2F15%29x%2B1%29 --> 15x=14x%2B15
Subtracting 14x from both sides of the equal sign:
15x=14x%2B15 --> 15x-14x=14x%2B15-14x --> highlight%28x=15%29