It must use a system of equations. There are 50 questions on a test. A correct answer is 2 points and an incorrect answer deducts 1/2 point. Fran answered all questions and received a score of 85. How many correct answers did Fran have?
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The answer is thirty-five ( 42.50x2=85 50.00-42.50=7.50 42.50 & 7.50= 50 7.50x.5=3.75 2x3.75= 7.5 85% & 15% +100 % since it was 1/2 point on each question wrong and 2 points on each right 15 x 50=7.5 and 42.50 & 7.50 =50 ) 50-15=35
answered 2 months ago
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Let
r = the number of right answers that Fran had, and
w = the number of wrong answers Fran had.
The system of equations:
r + w = 50 (there are 50 questions, each either right or wrong)
2r - (1/2)w = 85 (apply scoring rules to get Fran's score)
Solution:
add 2 times the second equation to the first
(r + w) + 2(2r - w/2) = 50 + 2(85)
r + 4r + w - w = 50 + 170
5r = 220
r = 220/5 = 44
Fran got 44 questions right.
Check
If Fran got 44 right, she got (50-44)=6 wrong.
2(44) - (1/2)(6) = 85
88 - 3 = 85 (yes)
answered 2 months ago
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