A student’s grade on Mrs. Sampson’s final exam varies directly with the number of problems a student answer correctly. Mark answered 30 problems correctly and earned a grade of 75%. Linda earned a grade of 100%.%0D%0A%0D%0AHow many problems did Linda answer correctly on the test?
Since the grade varies directly with the number of problems answered correctly, we can set up a proportion to solve for the number of problems Linda answered correctly.
Let x be the number of problems Linda answered correctly.
Using the information given:
Mark answered 30 problems correctly and earned a grade of 75%
This can be written as:
(Grade) / 100 = (Number of problems answered correctly) / Total number of problems
For Mark:
75 / 100 = 30 / Total number of problems
0.75 = 30 / Total number of problems
Total number of problems = 30 / 0.75
Total number of problems = 40
Now, we can set up the proportion for Linda:
100 / 100 = x / 40
1 = x / 40
x = 40
Therefore, Linda answered 40 problems correctly on the test.