SOLUTION: How do I solve. A baseball manager bought four bats and nine balls for $76.50. On another day, she bought three bats and twelve balls at the same prices and paid $81.00. How much d

Algebra ->  Graphs -> SOLUTION: How do I solve. A baseball manager bought four bats and nine balls for $76.50. On another day, she bought three bats and twelve balls at the same prices and paid $81.00. How much d      Log On


   

Question 1141823: How do I solve. A baseball manager bought four bats and nine balls for $76.50. On another day, she bought three bats and twelve balls at the same prices and paid $81.00. How much did she pay for each bat and each bsll?
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

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


 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)