SOLUTION: 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 system
Question 232543: 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? Answer by ankor@dixie-net.com(22740) (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?
;
Let x = no. of 5 pt problems
Let y = no. of 2 pt problems
;
The total problem equation
x + y = 38
or
y = (38-x); use this form for substitution in the next equation
:
Total points equation
5x + 2y = 100
Replace y with (38-x); find x
5x + 2(38-x) = 100
5x + 76 - 2x = 100
5x - 2x = 100 - 76
3x = 24
x =
x = 8 ea 5 point problems
then
38-8 = 30 ea 2 point problems
:
:
Check solutions in the total point equation
5(8) + 30(2) =
40 + 60 = 100
