Let C represent the number of students in your class last year and I represent the number of students in your class last year who played an instrument.
C
Practice makes perfect
Let C represent the number of students in the class last year and I be the number of students in the class last year who played an instrument. We know that last year 14 of the students played an instrument. Let's express this algebraically.
1/4 C= I
This year there are 6 new students, making the total number of students C+6. Of the new students, 4 play an instrument. There are now I+4 students playing an instrument. This change in classroom size made it so now 13 of the students play instruments. We can also write this as an equation.
1/3( C+6)= I+4
By combining these equations we get a system of equations.
14 C= I 13( C+6)= I+4
The first equation already has an isolated variable. Therefore, the preferred way to solve this system is with the Substitution Method. We can immediately substitute I for 14 C into Equation (II). Remember, when adding and subtracting fractions we need to have a common denominator.
For the purposes of this question, it is sufficient to only solve for C. With C= 24, we know that last year's class had 24 students. This year 6 new students joined the class, making the total number 24+6=30. This corresponds to option C.
