For the first 15 questions on a test, 14 questions were answered correctly but only 60% of the remaining questions was correctly answered. 4/5 of the whole test was correct. If each question was awarded of equal value, how many questions was there altogether?
If x more questions were answered correctly, then
14 + 3/5 x = 4/5 (15+x)
find x, and the total is thus x+15
To solve this problem, we can break it down step by step.
Let's assume there are a total of x questions on the test.
According to the information given, for the first 15 questions, 14 were answered correctly, which means there was one question answered incorrectly.
The remaining questions are x - 15.
We are told that only 60% of the remaining questions are answered correctly, which means 0.6 * (x - 15) questions were answered correctly.
Adding up the correctly answered questions in the first 15 questions and the correctly answered questions in the remaining questions, we get:
14 + 0.6 * (x - 15) = 4/5 * x
Let's solve this equation: