While on vacation a group can rent bikes and scooters by the week. They gett a reduced rental rate if they rent 5bikes for every two scooters rented. The reduced rate per bike is $15.50 amd the reduced rate per scooter is $160 a week. The sales tax on each rental is 12%.
The group has $1600 available to spend on bike amd scooter rentals. What is the greatest number of bikes amd the greatest number of scooters the group can rent if the ratio of bikes to scooters is 5:2?
PLEASE help and say how u got your answer!
5x = The # of bikes rented.
2x = The # of scooters renteb
15.50*1.12*5x + 160*1.12*2x = 1600.
86.8x + 358.4x = 1600
445.2x = 1600
X = 3.59
Bikes = 5 * 3.59 = 18
Scooters = 2 * 3.59 = 7.
To solve this problem, let's start by setting up an equation based on the given information.
Let:
- x = the number of bikes rented
- y = the number of scooters rented
According to the information given, the ratio of bikes to scooters is 5:2. This can be written as x:y = 5:2. We can express this ratio mathematically as x/y = 5/2.
Now, let's calculate the total cost for renting the bikes and scooters. The reduced rate per bike is $15.50, and the reduced rate per scooter is $160. Therefore, the cost for renting x bikes would be 15.50x, and the cost for renting y scooters would be 160y.
The group has $1600 available to spend on rentals, and we need to consider the 12% sales tax on each rental. So, the equation for the total cost, including tax, can be expressed as:
(15.50x + 160y) + 0.12(15.50x + 160y) = 1600
Now, let's simplify the equation:
15.50x + 160y + 0.12(15.50x + 160y) = 1600
15.50x + 160y + 1.86x + 19.20y = 1600
17.36x + 179.20y = 1600
Next, we will use the fact that x/y = 5/2 to solve for x or y in terms of the other variable. Since we are looking for the greatest number of bikes and scooters the group can rent, we should try to maximize x and y. This can be done by finding the largest possible common multiple of 5 and 2.
The largest common multiple of 5 and 2 is 10. Let's multiply both sides of the equation x/y = 5/2 by 10 to eliminate the fractions:
10(x/y) = 10(5/2)
10x/y = 25
Now, let's solve for x in terms of y:
10x/y = 25
10x = 25y
x = 2.5y
Now, substitute the value of x in terms of y in the simplified equation:
17.36x + 179.20y = 1600
17.36(2.5y) + 179.20y = 1600
43.4y + 179.20y = 1600
222.6y = 1600
y = 1600/222.6
y ≈ 7.18
Since the number of scooters must be a whole number, the greatest number of scooters the group can rent is 7.
Now, substitute the value of y back into the equation x = 2.5y to find the number of bikes:
x = 2.5(7)
x = 17.5
Since the number of bikes must also be a whole number, the greatest number of bikes the group can rent is 17.
Therefore, the greatest number of bikes the group can rent is 17, and the greatest number of scooters is 7.