SOLUTION: If the ratio of a to b is 4 to 5, find the value of the expression 2a+3b/4b-3a. Express your answer as a common or improper fraction reduced to lowest terms. Thanks for your help.

Algebra ->  Equations -> SOLUTION: If the ratio of a to b is 4 to 5, find the value of the expression 2a+3b/4b-3a. Express your answer as a common or improper fraction reduced to lowest terms. Thanks for your help.      Log On


   

Question 945636: If the ratio of a to b is 4 to 5, find the value of the expression 2a+3b/4b-3a. Express your answer as a common or improper fraction reduced to lowest terms. Thanks for your help.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


If the ratio of a to b is 4 to 5, then we have
a%2Fb=4%2F5+=>solve for a
a=%284%2F5+%29b
a=4b%2F5
to find the value of the expression
%282a%2B3b%29%2F%284b-3a%29 substitute 4b%2F5 for a

=%282%284b%2F5%29%2B3b%29%2F%284b-3%284b%2F5%29%29

=%288b%2F5%2B3b%29%2F%284b-12b%2F5%29

=%288b%2F5%2B15b%2F5%29%2F%2820b%2F5-12b%2F5%29

=%2823cross%28b%29%2Fcross%285%29%29%2F%288cross%28b%29%2Fcross%285%29%29

=23%2F8