Question

Tickets to a school play are $4.50 for an adult and $3.00 for a student. If 300 tickets are sold and $1087.50 collected, how many tickets of each were sold

Answer 1

125 tickets for an adult

and 175 tickets for a student

Explanation:

`a-\text{number of the tickets for an adult}\\s-\text{number of the tickets for a student}\\\\(1)\qquad a+s=300\\(2)\qquad4.5a+3s=1087.5\\------------\\(1)\\a+s=300\qquad\text{subtstitute}\ s\ \text{from both sides}\\a=300-s\\\\\text{Put it to (2):}\\\\4.5(300-s)+3s=1087.5\qquad\text{use distributive property}\\\\(4.5)(300)+(4.5)(-s)+3s=1087.5\\\\1350-4.5s+3s=1087.5\qquad\text{subtract 1350 from both sides}\\\\-1.5s=-262.5\qquad\text{divide both sides by (-1.5)}\\\\\boxed{s=175}`

`\text{Put the value of}\ s\ \text{to (1):}\\\\a=300-175\\\\\boxed{a=125}`