SOLUTION: A student missed 3 problems on a mathematics test and recieved a grade of 81%. if all the problems were of equal value, how many problems were on the test? Round off your answer to

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A student missed 3 problems on a mathematics test and recieved a grade of 81%. if all the problems were of equal value, how many problems were on the test? Round off your answer to      Log On


   

Question 414520: A student missed 3 problems on a mathematics test and recieved a grade of 81%. if all the problems were of equal value, how many problems were on the test? Round off your answer to the nearest interger
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Note: 81% in decimal form is 0.81 (drop the % and move the decimal 2 spots to the left)


Say there are x problems total.


So if you missed 3 problems, then that means you got x-3 problems correct. Eg: x=20, so you got x-3=20-3=17 problems correct


Now all we need to do is divide the number of problems you got correct by the total number of problems to get the decimal form of the percentage.


So we get %28x-3%29%2Fx=0.81


Now multiply both sides by x to get x-3=0.81x


Now let's solve for x


x-3=0.81x


-3=0.81x-x


-3=-0.19x


-3%2F%28-0.19%29=x


15.78947=x


So x=15.78947 (roughly). Round to the nearest whole number to get 16


So there are 16 problems total.


Note: this means that you got 16-3 = 13 problems correct. So 13/16 = 0.8125 which is close enough to 0.81 giving us the percentage 81%


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