Question

a total of 440 tickets were sold for the school play. they were either adult tickets or student tickets. there were 60 fewer student tickets sold than adult tickets. how many adult tickets were sold? question 2 of 28 dante will rent a car for the weekend. he can choose one of two plans. the first plan has an initial fee of $43.96 and costs an additional $0.15 per mile driven. the second plan has an initial fee of $51.96 and costs an additional $0.13 per mile driven. how many miles would dante need to drive for the two plans to cost the same?

Explanation:

First Problem (Ticket Sales)

Step1: Define variables

Let $x$ = number of adult tickets.
Student tickets = $x - 60$

Step2: Set up total ticket equation

$x + (x - 60) = 440$

Step3: Simplify and solve for $x$

$2x - 60 = 440$
$2x = 440 + 60 = 500$
$x = \frac{500}{2} = 250$

Step1: Define variables and cost functions

Let $m$ = number of miles driven.
Cost of Plan 1: $C_1 = 43.96 + 0.15m$
Cost of Plan 2: $C_2 = 51.96 + 0.13m$

Step2: Set costs equal to each other

$43.96 + 0.15m = 51.96 + 0.13m$

Step3: Isolate $m$ terms

$0.15m - 0.13m = 51.96 - 43.96$
$0.02m = 8$

Step4: Solve for $m$

$m = \frac{8}{0.02} = 400$

Answer:

250 adult tickets were sold.

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Second Problem (Car Rental Plans)