Exploring Systems in the Real World Answers

Anthony purchased 6 fruit bars and 3 chocolate-nut bars for a camping trip. He spent $4.12 on the bars. Anthony wrote the following equation: . What did he define as the variable x?

Jalynn and Emma enjoy hiking. Jalynn hikes 1 mile in 20 minutes. Emma hikes at a rate of 3 miles per hour. On Sunday at 8:00 a.m., they both left the trail head. The line representing Jaylynn’s progress is graphed. Which statements are true about the system that models this scenario?

Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line.How many solutions should Sudhanshu find?

Javier is comparing costs of two cars. Car A costs $130 per month for insurance and $0.10 per mile to run. Car B costs $108 per month for insurance and $0.15 per mile to run. He defines x as the number of miles driven each month and y as the total cost to run the car. Which set of equations can be used to find the number of miles Javier would need to drive to make the costs equal?

How many solutions does the system have?

Audra counted change collected for a class fundraiser. Audra wrote the equation to represent the situation. What did she define as the variable x?

Joe and Nate went for a walk. The system representing each boy’s progress is graphed below. Which statements about the system and scenario are true? Check all that apply.

Ben and Arnoldo are sharing snacks. They have peanut treats and coconut treats. Ben ate 2 of the peanut treats and 4 of the coconut treats for a total of 160 calories. Arnoldo ate 3 of the peanut treats and 2 of the coconut treats for a total of 140 calories. They wrote the system below to represent the number of calories there are in the two types of treats.They found the solution to be (30, 25). How many calories are in each treat?

Aisha bought 15 apples and oranges for $9.00. Each orange costs $0.50, and each apple costs $0.65. Let x represent the number of oranges and y represent the number of apples. Which system can be used to find the number of apples and oranges Aisha bought?

The mechanics at Giuseppe’s Auto House specialize in changing fuel injection units and transmissions. Last week, they changed 5 fuel injection units and 10 transmissions and billed 70 hours. This week, they changed 8 fuel injection units and 8 transmissions and billed 64 hours. Let x represent the number of hours to change a fuel injection unit and y represent the number of hours to change a transmission. What is the solution to the system that represents this scenario?