Systems Of Equations Word Problems

Example 1 CHS is selling tickets to the annual talent show. On the first day of ticket sales the school sold 4 senior citizen tickets and 5 student tickets for a total of $102. The school took in $126 on the second day by selling 7 senior citizen tickets and 5 student tickets. What is the price each of one senior citizen ticket and one student ticket? 4𝑐+5𝑠=102 7𝑐+5𝑠=126

Example 2 Wolfrich lived in Portugal and Brazil for a total period of 14 months in order to learn Portuguese. He learned an average of 130 new words per month when he lived in Portugal, and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words.  How long did Wolfrich live in Portugal and how long did he live in Brazil? 𝑝+𝑏=14 130𝑝+150𝑏=1920

Example 3 A stone falls from the top of a cliff into the ocean. In the air, it had an average speed of 16 m/s. In the water, it had an average speed of 3 m/s before hitting the seabed. The total distance from the top of the cliff to the seabed is 127 meters, and the stone's entire fall took 12 seconds.  How long did the stone fall in air and how long did it fall in the water? 16𝑎+3𝑤=127 𝑎+𝑤=12

Example 4 2𝑎+2𝑠+𝑐=52 𝑎+2𝑠+3𝑐=56 𝑎+4𝑐=44 A student-written performance is playing at CHS. Cole paid $52 for two adult, two student, and one child tickets; Cali paid $56 for one adult, two student, and three child tickets; and Tyson paid $44 for one adult and four child tickets. What is the price of each adult, student, and child ticket? 2𝑎+2𝑠+𝑐=52 𝑎+2𝑠+3𝑐=56 𝑎+4𝑐=44

Example 5 50𝑡+20𝑠+15ℎ=1350 𝑡 + 𝑠 + ℎ = 40 𝑡 = 𝑠 + ℎ An ultimate frisbee team has to order jerseys, shorts, and hats. They have a budget of $1350 to spend on $50 jerseys, $20 shorts, and $15 hats. They want to buy40 items in preparation for the upcoming season and must order as many jerseys as shorts and hats combined. 50𝑡+20𝑠+15ℎ=1350 𝑡 + 𝑠 + ℎ = 40 𝑡 = 𝑠 + ℎ

Exit Slip 25𝑡+10𝑐+5𝑏=105 𝑡 + 𝑐 + 𝑏 = 10 𝑏 = 𝑡 + 𝑐 Johnaon wants to buy something for himself with his pocket money. He has a budget of $105 to spend on $25 T-shirts, $10 CDs, and $5 books. He wants to buy 10 items and wants to buy as many books as T-shirts and CDs combined. 25𝑡+10𝑐+5𝑏=105 𝑡 + 𝑐 + 𝑏 = 10 𝑏 = 𝑡 + 𝑐

Exit Slip The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended? 1.50𝑐+4𝑎=5050 𝑐+𝑎=2200