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!

2 answers

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