SOLUTION: The booster club bought 29 tickets to a baseball game. some of the tickets cost 21 each and the others cost 27 each. the total cost was 675. how many os each kind of tickets did th

Algebra ->  Systems-of-equations -> SOLUTION: The booster club bought 29 tickets to a baseball game. some of the tickets cost 21 each and the others cost 27 each. the total cost was 675. how many os each kind of tickets did th      Log On


   

Question 235149: The booster club bought 29 tickets to a baseball game. some of the tickets cost 21 each and the others cost 27 each. the total cost was 675. how many os each kind of tickets did they buy?
Answer by Stitch(470) About Me  (Show Source):
You can put this solution on YOUR website!
Setup:
A = # of tiickets that cost $21
B = # of tickets that cost $27
Equation 1: 21%2AA+%2B+27%2AB+=+675
Equation 2: +A+%2B+B+=+29
Solution:
Solve equation 2 for one of the variables. I picked A
+A+%2B+B+=+29
+A+=+29+-+B
Now plug (29-B) into equation 1 for A
21%2AA+%2B+27%2AB+=+675
21%2A%2829-B%29+%2B+27%2AB+=+675 Simplify the equation
609+-+21B+%2B+27B+=+675 Simplify again
609+%2B+6B+=+675 Subtract 609 from both sides
6B+=+66 Divide both sides by 6
B+=+11
Now plug 11 into equation 2 for B
+A+%2B+B+=+29
+A+%2B+11+=+29
A+=+18
Check your answer
21%2AA+%2B+27%2AB+=+675
21%2A18+%2B+27%2A11+=+675
378+%2B+297+=+675
675+=+675