SOLUTION: Your teacher is giving you a test worth 100 points containing 40 questions on the test. There are 2point and 4 point questions. How many of each are there?

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: Your teacher is giving you a test worth 100 points containing 40 questions on the test. There are 2point and 4 point questions. How many of each are there?      Log On

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Question 162607: Your teacher is giving you a test worth 100 points containing 40 questions on the test. There are 2point and 4 point questions. How many of each are there?
Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!

x=number+of+2pts
y=number+of+4pts
Then, 2x%2B4y=100pts ---------------------------------------> EQN 1
Also, x%2By=40qts -----------------------------------------> EQN 2
In EQn 2, we get x=40-y ----------------------------------> EQN 3
Subst. EQN 3 in EQN 1:
2%2840-y%29%2B4y=100
80-2y%2B4y=100
2y=100-80=20
cross%282%29y%2Fcross%282%29=cross%2820%2910%2Fcross%282%29
y=10qts for 4pts
In EQN 3,
x=40-10=30qts for 2pts
In doubt? Go back EQN 1:
2%2A30%2B4%2A10=100pts
60%2B40=100
100pts=100pts
Thank you,
Jojo