Advance tickets for a school play went on sale.

Question

Advance tickets for a school play went on sale. The price of each student ticket was $4 and everyone else paid $5. On the first day, no more than $80 in tickets were sold. Describe and explain the possible values of s, the number of student tickets sold, and e, the number of tickets sold to nonstudents.

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Answer 1

4s + 5e = 80 is the main equation that relates the number of tickets sold of each type.

SOlving for s:

4s = 80 - 5e

s = (80 - 5e)/4

Solving for e:

e = (80 - 4s)/5

You can now find the of tickets of each type given the other type.

For example, if 4 non-student tickets were sold, then e=4 in the first formula:

s = (80 - 5*4)/4 = (80 -20)/4 = 60/4 = 15 student tickets were sold.

On the other hand, for example, if 10 student tickets were sold, then

s=10 and e = (80 -4*10)/5 = (80 - 40)/5 = 40/5 = 8 non-student tickets were sold.