SOLUTION: A conference spent $108 on 154 servings of cantaloupe and honeydew. If a cantaloupe melon costs $3 and serves four while a honeydew melon costs $4 and serves six, how many honeydew

Algebra ->  Matrices-and-determiminant -> SOLUTION: A conference spent $108 on 154 servings of cantaloupe and honeydew. If a cantaloupe melon costs $3 and serves four while a honeydew melon costs $4 and serves six, how many honeydew      Log On


   

Question 1167810: A conference spent $108 on 154 servings of cantaloupe and honeydew. If a cantaloupe melon costs $3 and serves four while a honeydew melon costs $4 and serves six, how many honeydew melons did the organizers buy?
Answer by ikleyn(52767) About Me  (Show Source):
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A conference spent $108 on 154 servings of cantaloupe and honeydew. If a cantaloupe melon costs $3 and serves four
while a honeydew melon costs $4 and serves six, how many honeydew melons did the organizers buy?
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Let x = the number of honeydew servings.

Then the number of the cantaloupe servings is (154-x).


Each single honeydew   serving costs 4%2F6 = 2%2F3  dollars;

Each single cantaloupe serving costs 3%2F4  dollars.


Write the money equation


    %282%2F3%29x+%2B+%283%2F4%29%2A%28154-x%29 = 108  dollars.


Multiply both sides by 12


    8x + 9*(154-x) = 12*108.


From the equation

  
    x = %2812%2A108-9%2A154%29%2F%288-9%29 = 90.


90 honeydew servings means  90%2F6 = 15  honeydew mellons.


ANSWER.  15  honeydew mellons.

Solved.