SOLUTION: Horses sold for $400 each and ponies for only $100. Weir spent $4500 and bought 5 more horses than ponies. How many horses did she buy?

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Question 1202547: Horses sold for $400 each and ponies for only $100. Weir spent $4500 and bought 5 more horses than ponies. How many horses did she buy?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!

              PRICE        QTY.       COST($)

HORSES         400          h          400h

PONIES         100         h-5        100(h-5)

Total                                   4500

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Answer by ikleyn(52921)   (Show Source): You can put this solution on YOUR website!
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Horses sold for $400 each and ponies for only $100.
Weir spent $4500 and bought 5 more horses than ponies. How many horses did she buy?
~~~~~~~~~~~~~~~ 

Let x be the number of the horses.

Then the number of the ponies is (x-5).


Write the total money equation

    400*x + 100*(x-5) = 4500  dollars.


Simplify and solve

    400x + 100x - 500 = 4500

        500x = 4500 + 500

        500x = 5000

           x = 5000/500 = 10.


ANSWER.  10 horses and 10-5 = 5 ponies.


CHECK.   Check the total cost  10*400 + 5*100 = 4500  dollars.   ! Precisely correct !

Solved.



Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!


While a formal algebraic solution was probably wanted, note that you can get good mental exercise, and good problem-solving practice, by solving the problem informally using logical reasoning and simple mental arithmetic.

In this problem, she bought 5 more horses than ponies. Those 5 "extra" horses cost 5($400) = $2000.

Beyond that, there were equal numbers of horses and ponies with a total cost of $4500-$2000 = $2500.

The cost of one horse and one pony is $400+$100 = $500; to make the additional $2500 cost, the remaining number of horses and ponies must have been $2500/$500 = 5.

So the number of ponies she bought was 5, and the number of horses she bought was 5+5 = 10.

ANSWER: 10 horses (and 5 ponies)

CHECK: 10($400)+5($100) = $4500
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