Question

Mohamed is selling tickets for his home movies. Tickets for friends are $3.00, and everyone else must pay $5.00 per ticket. If he sold 72 tickets and made $258, how many of each type did he sell?

A) 36 friend tickets and 36 non-friend tickets
B) 40 friend tickets and 32 non-friend tickets
C) 44 friend tickets and 28 non-friend tickets
D) 48 friend tickets and 24 non-friend tickets

Answer 1

Mohamed sold 51 friend tickets and 21 non-friend tickets.

Step-by-step explanation:

To solve this problem, we can use a system of equations to represent the given information:

Let x be the number of tickets sold to friends.

Let y be the number of tickets sold to non-friends.

We can then set up two equations to represent the total number of tickets sold and the total amount of money made:

1. x + y = 72 (equation 1)
2. 3x + 5y = 258 (equation 2)

We can solve this system of equations using substitution or elimination. Let's use elimination. Multiply equation 1 by 3 to match the coefficients of x:

1. 3x + 3y = 216 (equation 3)
2. 3x + 5y = 258 (equation 4)

Subtract equation 3 from equation 4 to eliminate the x variable:

1. 3x + 5y - 3x - 3y = 258 - 216
2. 2y = 42
3. y = 21

Substitute the value of y into equation 1 to solve for x:

1. x + 21 = 72
2. x = 51

Therefore, Mohamed sold 51 friend tickets and 21 non-friend tickets.