Question

Dylan works out and burns 10 calories per minute swimming and 7 calories per minute biking. He wants to burn a minimum of 600 calories. Due to daylight limitations, the time Dylan spends swimming must be no less than twice the time he spends biking.

Given that x is the number of minutes spent swimming and y is the number of minutes spent biking, determine which inequalities represent the constraints for this situation.Which combinations of minutes spent swimming and minutes spent biking satisfy this system of inequalities? Select all that apply.

Answer 1

Let x be the number of minutes spent swimming and y be the number of minutes spent biking.

Since the time Dylan spends swimming must be no less than twice the time he spends biking, you obtain the unequality
`x\ge 2y`

If Dylan works out and burns 10 calories per minute swimming, then he burns 10x calories per x minutes and if Dylan works out and burns 7 calories per minute biking, then he burns 7y calories per y minutes. He wants to burn a minimum of 600 calories, then total amount of calories he burns is
`10x+7y\ge 600`.
You have the following system:
`\left \{ {{x\ge 2y} \atop {10x+7y\ge 600}} \right.`. The graphical interpretation see on the picture.

Let's solve the system:
`\left \{ {{x=2y} \atop {10x+7y=600}} \right.`. If x=2y, then 20y+7y=600, 27y=600,
`y= (200)/(9)` and
`x= (400)/(9)` is the minimal number of minutes, that Dylan has to spend biking and swimming.

Also you can take any point from the shaded domian (see picture), for example x=70, y=20.