student missed 11 problems on a Chemistry test and received a grade of 65%. If all the problems were of equal value, how many problems were on the test? Round off your answer to the nearest integer.
X= # of problems
11= # of missed problems
65% of correct problems
35% of missed problms
11/0.35= 21 problems
To find the total number of problems on the test, we can set up a proportion using the information given.
Let's let X be the number of problems on the test. We know that the student missed 11 problems, so the number of correct problems is X - 11.
The grade received is 65%, so the fraction of correct problems is 65/100.
Setting up the proportion:
(X - 11) / X = 65/100
To solve this proportion, we can cross-multiply:
100(X - 11) = 65X
Expanding and simplifying:
100X - 1100 = 65X
Moving all the terms with X to one side:
100X - 65X = 1100
35X = 1100
Dividing both sides by 35:
X = 1100 / 35
X = 31.4286
Since the number of problems must be a whole number, we round off the answer to the nearest integer: 31.
Therefore, there were approximately 31 problems on the Chemistry test.