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Question 476566: Next week your math teacher is giving a chapter test worth 100 points. The test will consist of 35 problems. Some problems are worth 2 points and some problems are worth 4 points. How many problems of each value are on the test?)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = number of questions that are 2 points each.
let y = number of questions that are 3 points each.
since the total number of questions is 35, then your first equation is:
x + y = 35
since each x gets you 2 points and each y gets you 3 points, then your ssecond equation is:
2x + 3y = 100
solve these 2 equations simultaneously for your answer.
use second equation to solve for y in terms of x.
you get y = 35 - x
substitute for y in the first equation to get:
2x + 3(35-x) = 100 which becomes:
2x + 105 - 3x = 100 which becomes:
-x + 105 = 100
add x to both sides of this equation and subtract 100 from both sides of this equation to get:
x = 5
since x + y = 35, this means that y = 30
you have 5 questions that are 2 points each and 30 questions that are 3 points each for a total of 5 + 30 = 35 questions with a total of 10 + 90 = 100 points.
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