Question

question 6 of 6 (1 point) | question attempt: 1 of 1
tammy can choose plan a or plan b for her long distance charges. for each plan, cost (in dollars) depends on minutes used (per month) as shown below.
graph of cost (in dollars) vs. minutes used (per month) with plan a (blue line through origin) and plan b (red horizontal line starting at (0,28))
(a) if tammy makes 50 minutes of long distance calls for the month, which plan costs more?
∘ plan a ∘ plan b
how much more does it cost than the other plan?
$blank
(b) for what number of long distance minutes do the two plans cost the same?
blank
if the time spent on long distance calls is less than this amount, which plan costs more?
∘ plan a ∘ plan b

Explanation:

Part (a)

Step 1: Find cost for Plan A at 50 minutes

Plan A is a line through the origin, so its equation is \( y = mx \). From the graph, when \( x = 450 \), \( y = 36 \) (approx, but at \( x = 50 \), let's see the slope. Wait, actually, at \( x = 0 \), \( y = 0 \), and at \( x = 50 \), let's check the graph. Wait, Plan A is a straight line from (0,0) to (450, 36)? Wait no, the graph: Plan A is blue, starts at (0,0), goes up. Plan B is red, horizontal line at \( y = 28 \). Wait, at \( x = 50 \), Plan A: let's calculate the slope. The slope \( m \) for Plan A: when \( x = 450 \), \( y = 36 \), so \( m = \frac{36}{450} = 0.08 \) dollars per minute. So at \( x = 50 \), cost for Plan A is \( 0.08 \times 50 = 4 \) dollars? Wait no, wait the y-axis: at x=0, Plan A is 0, Plan B is 28. At x=50, Plan A: let's see the graph. Wait, the y-axis has 0,4,8,12,16,20,24,28,32,36. So at x=50, Plan A is at y=4? Wait no, the line for Plan A: from (0,0) to (450, 36). So the equation is \( y = \frac{36}{450}x = 0.08x \). So at x=50, y=0.08*50=4. Plan B is always 28 dollars (horizontal line). So Plan B costs 28, Plan A costs 4. So Plan B costs more. The difference is 28 - 4 = 24.

Step 2: Determine which plan costs more and the difference

Plan B costs 28, Plan A costs 4. So Plan B is more. Difference: 28 - 4 = 24.

Part (b)

Step 1: Find intersection of Plan A and Plan B

Plan A: \( y = 0.08x \) (from slope calculation: 36/450 = 0.08). Plan B: \( y = 28 \). Set equal: \( 0.08x = 28 \). Solve for x: \( x = \frac{28}{0.08} = 350 \). So at 350 minutes, both cost the same.

Step 2: Determine which plan costs more for less than 350 minutes

For x < 350, let's take x=0: Plan A is 0, Plan B is 28. So Plan B costs more when x < 350? Wait no, wait at x=50, Plan A is 4, Plan B is 28. So when x < 350, Plan B (28) is more than Plan A (which is less than 28, since at x=350, Plan A is 28). Wait, at x=350, Plan A: 0.08*350 = 28, which equals Plan B. So for x < 350, Plan A's cost is less than 28, and Plan B's cost is 28. So Plan B costs more when x < 350. Wait, but the question is: "If the time spent on long distance calls is less than this amount (350), which plan costs more?" So Plan B.

Answer:

(a) The plan that costs more is Plan B. The difference is $24.
(b) The two plans cost the same at 350 minutes. For less than 350 minutes, Plan B costs more.

Final Answers:

(a) Plan B, $24
(b) 350 minutes, Plan B