SOLUTION: a professor has two types of problems to use in putting together a test: multiple choice questions worth 1 point each and short answer questions worth 8 points each. If the profess

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: a professor has two types of problems to use in putting together a test: multiple choice questions worth 1 point each and short answer questions worth 8 points each. If the profess      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 802468: a professor has two types of problems to use in putting together a test: multiple choice questions worth 1 point each and short answer questions worth 8 points each. If the professor wants to create a 130 point test using a total of 74 questions, then how many question of each type should she use?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of +1+ point questions
Let +b+ = number of +8+ point questions
-----------
(1) +a+%2B+b+=+74+
(2) +1%2Aa+%2B+8%2Ab+=+130+
----------------------
Subtract (1) from (2)
(2) +a+%2B+8b+=+130+
(1) +-a+-+b+=+-74+
+7b+=+56+
+b+=+8+
and, since
(1) +a+%2B+8+=+74+
(1) +a+=+66+
66= number of +1+ point questions
8 = number of +8+ point questions
---------
check:
(2) +66+%2B+8%2A8+=+130+
(2) +66+%2B+64+=+130+
(2) +130+=+130+
OK