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Write a system of inequalities to represent the situation. One inequality should represent the total amount of time driving, one should represent the distance covered, and one will represent the fact that your friend drives more hours than you.
Example Solution: 4 hours by you and 6 hours by your friend
For this exercise we can write and graph a system of inequalities. The system will have three inequalities.
For all three inequalities we will let x represent the number of hours we drive and y represent the number of hours our friend drives.
at leastcan be interpreted as greater than or equal to and represented with ≥. Then, we have the following inequality. 70x +60y ≥ 600 Inequality (III): It is given that our friend drives more than us. We can write the following equality. y>x
With these inequalities we can write the following system. x+y < 15 70x +60y ≥ 600 y>x
To determine the number of hours we friend can drive we can graph the system created above. The solution to the system will be the intersection of the solution sets of all three inequalities. Let's graph each inequality on its own first.
To graph the first inequality we need to first graph the boundary line. We need to write the inequality as though it were a line in slope-intercept form. x+y = 15 ⇒ y = - x+15 Note, because the symbol is < our boundary line should be dashed.
LHS-70x=RHS-70x
.LHS /60.=.RHS /60.
Write as a sum of fractions
Calculate quotient
Put minus sign in front of fraction
a* b/c=a/c* b
a/b=.a /10./.b /10.
To graph the third and final inequality we will once again begin by graphing the boundary line. Note, because the symbol is > our boundary line should be dashed.
If we show all of these individual solution sets on the same coordinate plane, we have the following graph.
Any point contained in the above shaded area will be a solution for how many hours we and our friend can drive in a day without driving more than 15 hours and going at least 600 miles. Let's write some example solutions. &4 hours by you and 6 hours by your friend &2 hours by you and 8 hours by your friend &0 hours by you and 12 hours by your friend