Pedro is doing math exercises from a software program he recently purchased. In the program, you have to get at least 70% of the problems in an exercise right in order to gain proficiency. So far, Pedro answered one question, and he didn't get it right. Suppose he answers 75% of the following q questions correctly and gains proficiency in the exercise. Write an inequality in terms of q that models the situation.

The inequality would be
0.75q ≥ 0.70(q+1)

q is defined as the number of questions he answers after the first one. We are told he gets 75% of those correct; 75%=75/100=0.75. This gives us 0.75q.

Since he gains proficiency on the exercises, the total number he gets correct has to be at least 70%. This means the inequality would have the symbol greater than or equal to, as it cannot be less and have him gain proficiency.

He has already answered 1 question and answers q more; this gives us a total of q+1. Since he gains proficiency, the cutoff was 70%; 70%=70/100=0.70. This gives us the expression 0.70(q+1).

Our total inequality would then be 0.75q ≥ 0.70(q+1)