Respuesta :
Answer:
Step-by-step explanation:
determine which talk and text plan is better based on the number of text messages you send per month, we need to compare the total cost of each plan given a budget of $75 per month.
Let's analyze both plans:
Talk and Text Plan A:
Monthly service fee: $20
Cost per minute: $0.05
Cost for 250 texts: $20
Total cost = Monthly service fee + (Cost per minute * number of minutes) + Cost for texts
Total cost = $20 + ($0.05 * minutes) + $20
Talk and Text Plan B:
Monthly service fee: $20
First 100 minutes free, then $0.10 per minute
Cost for 200 texts: $15
Total cost = Monthly service fee + (Cost per minute * number of minutes after the first 100 minutes) + Cost for texts
Total cost = $20 + ($0.10 * (minutes - 100)) + $15
Given a budget of $75 per month, we need to determine the number of minutes we can afford under each plan, considering the cost of texts as well.
For Plan A:
20
+
(
0.05
×
minutes
)
+
20
≤
75
20+(0.05×minutes)+20≤75
0.05
×
minutes
≤
35
0.05×minutes≤35
minutes
≤
35
0.05
minutes≤
0.05
35
minutes
≤
700
minutes≤700
For Plan B:
20
+
(
0.10
×
(
minutes
−
100
)
)
+
15
≤
75
20+(0.10×(minutes−100))+15≤75
0.10
×
(
minutes
−
100
)
≤
40
0.10×(minutes−100)≤40
(
minutes
−
100
)
≤
40
0.10
(minutes−100)≤
0.10
40
minutes
−
100
≤
400
minutes−100≤400
minutes
≤
500
minutes≤500
So, under Plan A, you can afford up to 700 minutes if you spend $75 per month, while under Plan B, you can afford up to 500 minutes.
Now, let's compare the number of texts included in each plan:
Plan A offers 250 texts for $20.
Plan B offers 200 texts for $15.
Since both plans offer fewer than 500 texts, the number of texts included does not affect the decision.
Based on the analysis, if you send a moderate number of text messages per month and want to maximize the number of minutes you can use within a $75 budget, Plan A would be the better choice, as it allows for more minutes (700 minutes) compared to Plan B (500 minutes).