If 72 cupcakes must be divided equally among the students in a certain class, how many students are in the class?
(1) If the number of students is reduced by one-third, each student will receive 3 more cupcakes.
(2) If the number of cupcakes is doubled, each student will receive 12 cupcakes.

Now according to question number of students are reduced by [tex]\frac{1}{3}[/tex], then cupcakes received by each individual students is reduced by 3

So new number of students [tex]=N-\frac{N}{3}=\frac{2N}{3}[/tex]

Now according to question [tex]\frac{72}{\frac{2N}{3}}=N-3[/tex]

[tex]=216=2N^2-6N[/tex]

[tex]2N^2-6N-216=0[/tex]

N = 12 and N = -9

As students can not be negative so N = 12

(B) Now according to second question

[tex]72\times 2=12N[/tex]

N = 12 students

If 72 cupcakes must be divided equally among the students in a certain class, how many students are in the class? (1) If the number of students is reduced by one-third, each student will receive 3 more cupcakes. (2) If the number of cupcakes is doubled, each student will receive 12 cupcakes.

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If 72 cupcakes must be divided equally among the students in a certain class, how many students are in the class?
(1) If the number of students is reduced by one-third, each student will receive 3 more cupcakes.
(2) If the number of cupcakes is doubled, each student will receive 12 cupcakes.