SOLUTION: Your math teacher tells you that next week's test is worth 100 points and contains 38 problems. Each problem is worh either 5 points or 2 points. Because you are studying systems o

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Question 132010This question is from textbook Algebra 1
: Your math teacher tells you that next week's test is worth 100 points and contains 38 problems. Each problem is worh either 5 points or 2 points. Because you are studying systems of linear equations, your teacher says that for extra credit you can figure out how many problems of each value are on the test. How many of each value are there? This question is from textbook Algebra 1

Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
5x+%2B+2%2A%2838+-+x%29+=+100
5x+%2B+76+-+2x+=+100
3x+=+24
x+=+8
38+-+x+=+30
There are 8 questions worth 5 points and 30 questions worth 2 points
check:
5x+%2B+2%2A%2838+-+x%29+=+100
5%2A8+%2B+2%2A%2838+-+8%29+=+100
40+%2B+60+=+100
100+=+100
OK

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Your math teacher tells you that next week's test is worth 100 points and contains 38 problems. Each problem is worth either 5 points or 2 points. Because you are studying systems of linear equations, your teacher says that for extra credit you can figure out how many problems of each value are on the test. How many of each value are there?
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Let # of 5 point questions be "x" ; # of points available is 5x
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# of 2 point questions is "38-x" ; # of points available is 2(38-x)=76-2x
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EQUATION:
5x + 76 -2x = 100
3x = 24
x = 8 (# of 5-point questions)
38-x = 30 (# of 2-point questions)
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Cheers,
Stan H.