Question

Dominick is training for a race. He spends 0.75 hours running each time he runs and 1.5 hours swimming each time he swims. This week, he spent more than 6 hours training for the race. Which graph represents his possible training times this week?

A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 10, and number of swims on the y-axis, from 0 to 5. A dashed straight line with a negative slope goes through (0, 4) and (8, 0). Everything to the right of the line is shaded.

A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 10, and number of swims on the y-axis, from 0 to 5. A dashed straight line with a negative slope goes through (0, 4) and (8, 0). Everything to the left of the line is shaded.

A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 5, and number of swims on the y-axis, from 0 to 10. A dashed straight line with a negative slope goes through (0, 8) and (4, 0). Everything to the right of the line is shaded.A graph titled Dominick apostrophe s Training shows number of runs on the x-axis, from 0 to 5, and number of swims on the y-axis, from 0 to 10. A dashed straight line with a negative slope goes through (0, 8) and (4, 0). Everything to the left of the line is shaded.

Answer 1

Let x = number of runs and y = number of swims. Total time is 0.75x + 1.5y > 6. Multiply by 4: 3x + 6y > 24, or x + 2y > 8.

The boundary x + 2y = 8 passes through (0,4) and (8,0). Because the inequality is ">" (strict), the boundary is dashed and the region away from the origin (where x + 2y is larger) is shaded.

That matches the first graph: dashed line through (0,4) and (8,0) with everything to the right of the line shaded.