For a senior project, Brad must complete an internship in a career of his choice. To complete the internship, he must earn more than 40 hours of job shadowing in his chosen career. Brad can earn his internship hours by working a half-day (four hours) or a full-day (eight hours).

Which of the following graphs represents the number of half-days and full-days that Brad must work?

W.
X.

Y.
Z.
A.
W
B.
X
C.
Y
D.
Z

1 answer

To represent the number of half-days (4 hours) and full-days (8 hours) that Brad must work to exceed 40 hours of job shadowing, we need to express this in an equation.

Let:

  • \( h \) = number of half-days
  • \( f \) = number of full-days

The total hours can be expressed as:

\[ 4h + 8f > 40 \]

Simplifying this inequality, we can divide everything by 4:

\[ h + 2f > 10 \]

This inequality indicates that the total number of half-days \( h \) plus twice the number of full-days \( f \) must be greater than 10.

To represent this graphically:

  1. The line \( h + 2f = 10 \) would serve as the boundary, and we need to shade the area above this line (since we want values greater than 10).
  2. The graph must account for only non-negative solutions, meaning \( h \geq 0 \) and \( f \geq 0 \).

Now, we can evaluate the options based on these criteria:

  • The boundary line (when plotted) should increase, reflecting more hours with more full-days or half-days.
  • The feasible region should be in the first quadrant (where both \( h \) and \( f \) are non-negative) and above the line \( h + 2f = 10 \).

Without seeing the actual graphs (W, X, Y, Z), you will need to identify which one has:

  • A line representing \( h + 2f = 10 \)
  • The area above this line
  • Only non-negative values (first quadrant)

If you can provide descriptions or features of those graphs, we can further help identify the correct one.