Question 998986: A student missed 4 problems on a History test and received a grade of 85%. If all the problems were of equal value, how many problems were on the test?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = number of problems on the test.
then x-4 = number of problems you got correct.
since 85% / 100 = .85, the formula you would use is:
(x-4) / x = .85
multiply both sides of this equation by x to get:
x-4 = .85 * x
subtract .85 * x from both sides of this equation and add 4 to both sides of this equation to get:
x - .85 * x = 4
simplify to get:
.15 * x = 4
divide both sides of this equation by .15 to get:
x = 4 / .15
simplify to get:
x = 26.66667
since x has to be an integer, and 26.66667 rounds to 27, then you would choose 27 as your answer.
when x = 27, 27-4 = 23, and 23/27 = .8518.
multiply that by 100 to get 85.18% and round to the nearest percent to get 85%.
note that the answer could also have been 26, but since 27 is closer to 26.66667, you would choose 27.
if x = 26, then x-4 = 22, and 22/26 = .8462.
multiply that by 100 to get 84.62% and round to the nearest percent to get 85%.
both 26 and 27 round to 85%, but 27 is closer, so you would choose 27.
the assumed requirements of the problem are that the number of problems has to be an integer.
there is no such requirement for the grade, so the only requirement for the grade is that it rounds to 85%.
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