Word problem for Algebra 9th grade

Question

There are two schools going to Math competition, and 68 students have entered. There are two different competitions that day and some students have only entered 'up to algebra two', some only entered 'all the way to AP Calculus', and some have entered both.

How many of the team members are only entering 'all the way to AP Calculus'

Answer 1

To solve this, we also need the other information from your other posting of this question.

Up to Algebra 2: 38 Both:9 AP Calculus:?

(https://www.wyzant.com/answers/9343/up_to_algebra_2_38__both9___ap_calculus)

The students are divided into three groups: (a) those who entered "up to algebra 2", (b) those who entered AP calculus, and (c) those who entered both.  To find group (b), we must find the number of students who are not in groups (a) or (b).  We can use an equation in the following form:

("algebra 2" group) + ("both" group) + ("AP" group) = (total students)

Substituting the values given, and using a for the AP group, we have

38 + 9 + a = 68

47 + a = 68

a = 68-47 = 21