Mathematical Problem Solving

The cost of 5 boxes of envelopes and 6 boxes of notepaper is $16.75. Three boxes of envelopes and 4 boxes of notepaper cost $10.75. Find the cost of each box of envelopes and each box of notepaper.

The cost of 24 oranges and 15 apples is $12.36. Fifteen oranges and 12 apples cost $8.67. Find the cost of each orange and each apple.

The admission fee for a county fair is $4.00 for adults and $1.50 for children. On a certain day 2200 people attended the fair and $5050 is collected. How many children and adults attended?

During a special afternoon movie, a theater charges $4.00 for an adult ticket and $2.00 for a child’s ticket. That afternoon 380 tickets were sold for a total of $1320. How many children attended the movie?

A car salesman sold a total of 20 cars and trucks in a month and made $2500 in commission. He made $100 commission for each car and $200 commission for each truck he sold. How many cars and trucks did he sell?

Tickets to a movie cost $7.25 for adults and $5.50 for students. A group of people purchased 8 tickets for $52.75. How many adult tickets and student tickets were purchased?

The PTA is hosting the next dance. They would like to make at least a $600 profit from selling tickets. They estimate at most 350 students will attend the dance. They will earn $4 for each advanced ticket sold and $5 for each ticket sold at the door. Create and graph a system of inequalities for the system.

If 50 students buy tickets in advance and 100 buy tickets at the door, will the PTA meet its goal? How do you know?

The SCA is hosting the dance after that. They would like to make at least an $800 profit from selling tickets. They estimate at most 250 students will attend the dance. They will earn $5 for each advanced ticket sold and $7 for each ticket sold at the door. Create and graph a system of inequalities for the system.

If 50 students buy tickets in advance and 100 buy tickets at the door, will the SCA meet its goal? How do you know?