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

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) (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)



----



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



----

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) 

RELATED QUESTIONS

A baseball manager bought 4 bats and 9 balls for $33.75. On another day, he bought 3 bats  (answered by josmiceli)
The town recreation department ordered a total of 100 balls and bats and hats for the... (answered by stanbon)
Three baseball bats and five baseball gloves cost $235. Two bats and six gloves cost... (answered by greenestamps)
Three baseball bats and five baseball gloves cost $235. Two bats and six gloves cost... (answered by algebrahouse.com,greenestamps)
I really need HELP! Week 4 Application Assignment Answer the following questions. In 2004  (answered by Theo)
A baseball player gets 16 hits in 50 at bats.  What percent are hits and what percent are  (answered by mangopeeler07)
Assuming the factory manufactures bats for 6 hours a day, what is the rate of production... (answered by josgarithmetic)
Susan and Betsy bought sport supplies for summer camp. Susan bought six basketballs and... (answered by Cromlix)
Method of Elimination  Word Problem
8. Mehrab works in a department store selling sports  (answered by tvandenberg)