SOLUTION: A test has 18 questions and some are worth 4 marks each and some are worth 5 marks each; the child scores 83 overall on the test. How many questions were worth 5 marks?

Question 1029612: A test has 18 questions and some are worth 4 marks each and some are worth 5 marks each; the child scores 83 overall on the test. How many questions were worth 5 marks?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Call the number of 4-mark and 5-mark questions, x and y.
Then we can write
x + y = 18 and
4x + 5y = 83
Now multiply the top one by 4 and subtract and we get
4x + 5y = 83
-(4x + 4y = 72)
-----------------
y = 11
so that x = 7
Then the answer is 11 5-mark questions.
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