Systems of equations

Question

You and your nine friends have decided to take a few days to go camping. You are planning a recreational budget of $50 per day for activities. One day your group is consis the nearby amusement park. The bumper cars cost $3 per hour and two people can ride in each car . Another choice is the wat slide . The cost is $8 per person . How many bumper car and water slide tickets can you purchase for the group and stay within your budget ?

Answer 1

Let b = number of bumper car tickets purchased and w = number of water slide tickets purchased.

 

C = total cost = 3 b + 8 w <= 50 -- the only equation we have from the information you gave. Let us assume that each person takes exactly one ride. Furthermore, we assume that no one rides the bumper car for more than an hour. With these assumptions if n people ride the bumper car, 10 - n people ride the water slide.

 

Now 50 >= 3/2 n + 8*(10-n) --> note that the number of bumper car rides is half the number of people who ride on the bumper cars.

 

Hence 50 >= 80 - 13/2 n, or 13/2 n >= 30, or n >= 60/13 --> the minimum allowable integer value of n is 5. However, two people ride on a bumper ticket, so we need to choose an even integer for n and we choose the smallest allowable value of 6. This implies that 6/2 = 3 bumper car ride tickets and 10-6 = 4 water slide tickets were purchased for a cost of $41.