SOLUTION: A man bought 18 fruits. Some cost $1.50 each and the remainder cost $2.00 each. He spent a cost of $32.50. How many of each fruit did he buy?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A man bought 18 fruits. Some cost $1.50 each and the remainder cost $2.00 each. He spent a cost of $32.50. How many of each fruit did he buy?      Log On


   

Question 1034902: A man bought 18 fruits. Some cost $1.50 each and the remainder cost $2.00 each. He spent a cost of $32.50. How many of each fruit did he buy?
Answer by ikleyn(52926) About Me  (Show Source):
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A man bought 18 fruits. Some cost $1.50 each and the remainder cost $2.00 each. He spent a cost of $32.50. How many of each fruit did he buy?
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Let x = # of fruits that cost $1.50 each.
Then the number of fruits that cost $2.00 is 18-x.

x fruits by $1.50 each cost 1.50*x dollars.
(18-x) fruits by $2.00 each cost 2.00*(18-x).

So, you have this equation

1.5x + 2*(18-x) = 32.50.

Simplify and solve it:

1.5x + 36 - 2x = 32.50,

-0.5x = 32.50 - 36,

-0.5x = - 3.5,

x = %28-3.5%29%2F%28-0.5%29 = 7.

Answer. 7 fruits by $1.50 and (18-7) = 11 fruits by $2.00.

Check.  1.50*7 + 2.00*11 = 10.50 + 22.00 = 32.50.   Correct!