Question 1141823

There is enough information to write two equations with two unknowns.  That should allow you to solve for both variables.

<pre>
 Let x = price of one bat, in cents
 and y = price of one ball, in cents

(1)  4x + 9y = 7650     (from the first sentence, using 7650 cents = $76.50)
(2)  3x + 12y = 8100    (from the 2nd sentence)

We want to get the coefficient of one of the variables (say x) to be the same.
Start by multiplying (1) by  3:

(1')  12x + 27y = 22950

Multiply (2) by 4:
(2')  12x + 48y = 32400

Subtract (1') from (2'):

       0x + 21y = 9450
              y = 9450/21 = 450   (one ball costs $4.50)

Plug in y=450 into (1):  4x + 9(450) = 7650
                         4x + 4050 = 7650
                          4x = 3600
                           x = 900   (each bat costs $9.00)

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Ans:  Each ball costs $4.50, each bat costs $9.00

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Check:
     4*(9.00) + 9*(4.50) = 36 + 40.50 = 76.50   (first day purchase checks out)
     3*(9.00) + 12*(4.50) = 27 + 54 = 81.00   (2nd day purchase checks out)