Question

40 point.!!!! HELP ME PLEASE MY MOM GONNA YELL AT ME

Introduction Gwen is exercising at the gym. After a while, Tristan and Keith arrive to exercise with her. After they finish exercising, they are going to go to the fair.
In this activity, you will write a system of equations to determine if and when Gwen will have burned the same number of calories as Tristan and Keith. Then, you will write a system of equations to determine how much each ticket at the fair costs.
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Directions and Analysis Task 1: Solving Systems of Equations Graphically
Gwen, Tristan, and Keith like to work out at the gym. They each have an app on their phone that estimates the calories they burn. By the time Tristan and Keith started exercising, Gwen had already burned 100 calories. Gwen burns 10 calories every minute, Tristan burns 125 every 10 minutes, and Keith burns 300 calories every 30 minutes. Let x represent the number of minutes since Tristan and Keith started exercising and y represent the number of app-estimated calories burned.

a. Write an equation representing Gwen’s calories burned with respect to the number of minutes since Tristan and Keith started exercising.

b. Write an equation representing the number of calories Tristan has burned with respect to the number of minutes since he and Keith started exercising.

c. Write an equation representing the number of calories Keith has burned with respect to the number of minutes since he and Tristan started exercising.

Answer 1

Question 1)

Gwen has already burned 100 calories when Tristan and Keith started, and he continues to burn 10 calories per minute. The equation for Gwen is

y = 100 + 10x

Question 2)

`Tristan is burning 125 calories every 10 minutes. His burning calories rate is 12.5 calories per minute. The equation for Tristan is

y = 12.5x

Question 3)

Keith is burning 300 calories in 30 minutes. His rate per minute is 10 calories per minute. The equation for Keith is

y = 10x

Answer 2

Question 1)

Gwen has already burned 100 calories when Tristan and Keith started, and he continues to burn 10 calories per minute. The equation for Gwen is

y = 100 + 10x

Question 2)

`Tristan is burning 125 calories every 10 minutes. His burning calories rate is 12.5 calories per minute. The equation for Tristan is

y = 12.5x

Question 3)

Keith is burning 300 calories in 30 minutes. His rate per minute is 10 calories per minute. The equation for Keith is

y = 10x