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!
Well first of all you need to figure out the sales tax for one bike and one scooter .With the sales tax taken into consideration, one bike would cost $17.36. One scooter would cost $179.20. Then you need to figure out how much it would cost for 5 bikes and 2 scooters. Multiply $17.36 by 5 and you get $86.80. Multiply $179.20 by 2 and you get $358.40. Add $86.80 and $358.40 together to get $445.20. Next subtract $445.20 from $1600 to get $1154.80. That's how much money they have left so subtract another $445.20 to get 709.60. Now they have rented 10 bikes and 4 scooters. Subtract another $445.20 to get 264.44. Now they have rented 15 bikes and 6 scooters. Since they don't have enough to rent anymore bikes or scooters you are done. So the answer is 15 bikes and 6 scooters.
Hope this helps.
or, algebraically, we want
((15.50)(5x) + (160)(2x))(1.12) = 1600
x = 3.59
since fractional vehicles are not rented, that gives us
5*3 = 15 bikes
2*3 = 6 scooters
To find the maximum number of bikes and scooters the group can rent given the budget and the ratio of 5 bikes for every 2 scooters, we need to analyze the costs and see how they fit within the available budget.
Let's start by calculating the cost for each bike and scooter at the reduced rate, including the sales tax:
Cost per bike per week = Reduced rate per bike + Sales tax on each rental
= $15.50 + 12% of $15.50
= $15.50 + $1.86
= $17.36
Cost per scooter per week = Reduced rate per scooter + Sales tax on each rental
= $160 + 12% of $160
= $160 + $19.20
= $179.20
Now, we want to find the maximum number of bikes (5) and scooters (2), such that the total cost is within the available budget of $1600.
Let's assume the number of bikes rented is 5x, and the number of scooters rented is 2x, where x is a positive integer.
Total cost = Cost per bike per week * Number of bikes rented
+ Cost per scooter per week * Number of scooters rented
From the given information, the total cost must be less than or equal to $1600:
$17.36 * 5x + $179.20 * 2x ≤ $1600
Now we can solve the inequality to find the maximum value of x:
86.8x + 358.4x ≤ 1600
445.2x ≤ 1600
x ≤ 1600 / 445.2
x ≤ 3.59
Since we need a positive integer value for x, the maximum value x can take is 3.
Therefore, the group can rent a maximum of 5 * 3 = 15 bikes and 2 * 3 = 6 scooters within their budget of $1600.
To find the greatest number of bikes and the greatest number of scooters the group can rent within their budget, we need to set up an equation based on the given information.
Let's assume the number of bikes rented as 5x and the number of scooters rented as 2x (since the ratio of bikes to scooters is given as 5:2). The reduced rental rate per bike is $15.50 and the reduced rate per scooter is $160.
The total cost of renting bikes would be (5x * $15.50), and the total cost of renting scooters would be (2x * $160).
So, the equation representing the cost of renting bikes and scooters would be:
(5x * $15.50) + (2x * $160) = $1600
Now, let's solve this equation to find the value of x, which will give us the number of bikes and scooters the group can rent.
(5x * $15.50) + (2x * $160) = $1600
77.5x + 320x = $1600
397.5x = $1600
x ≈ 4.03
Now, we need to round down the value of x since we cannot rent a fraction of a bike or scooter. So, x = 4.
Finally, substituting this value back into our assumption, we get:
Number of bikes = 5x = 5 * 4 = 20
Number of scooters = 2x = 2 * 4 = 8
Therefore, the greatest number of bikes the group can rent is 20, and the greatest number of scooters they can rent is 8.