SOLUTION: A biology test has 25 problems. some are worth 2 points,and some are worth 3 points. the test is worth 60 points total. using a system of equations, determine the number of 2-point

Algebra ->  Average -> SOLUTION: A biology test has 25 problems. some are worth 2 points,and some are worth 3 points. the test is worth 60 points total. using a system of equations, determine the number of 2-point      Log On


   



Question 1006951: A biology test has 25 problems. some are worth 2 points,and some are worth 3 points. the test is worth 60 points total. using a system of equations, determine the number of 2-point problems and the number of 3-point problems on the test.
Thank You So Much!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the number of 2-point problems
Let +b+ = the number of 3-point problems
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(1) +a+%2B+b+=+25+
(2) +2a+%2B+3b+=+60+
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Multiply both sides of (1) by 2
and subtract (1) from (2)
(2) +2a+%2B+3b+=+60+
(1) +-2a+-+2b+=+-50+
--------------------
+b+=+10+
and
(1) +a+%2B+b+=+25+
(1) +a+%2B+10+=+25+
(1) +a+=+15+
There are 15 2-point problems and
There are 10 3-point problems
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check:
(2) +2a+%2B+3b+=+60+
(2) +2%2A15+%2B+3%2A10+=+60+
(2) +30+%2B+30+=+60+
(2) +60+=+60+
OK