The Cost of installing new kitchen cabinets is $150 for delivery for all the cabinets and an additional $45 to install each cabinet.
a) Develop a model to give the total cost for a set of n cabinets.
b) What is the total cost for a set of 18 cabinets?
c) Find the number of cabinets if the total cost was $735.
AND (2nd Question)
Membership in a tennis club costs $600 per year plus a $15 fee for each hour of court time.
a) Find a model that gives the total cost of playing tennis for h hours at this club in a year.
AND (3rd Question)
CoolCar rental agency charges $30 per day plus $.25 per mile.
a)Find a formula to compute the total cost of renting a car for on day and driving it for m miles.
You're more likely to get help if you post your answers and the parts you don't understand.
150 + cost per cabinet * number of cabinets
thus if n cabinets then
C = 150 + 45 n
C for 18 = 150 + 45 * 18
then 735 = 150 + 45 n
solve for n
Do the second one the same way.
a) To develop a model to give the total cost for a set of n cabinets, we need to consider the cost of delivery plus the cost of installing each individual cabinet.
The cost for delivery is $150 for all the cabinets. This is a fixed cost and does not depend on the number of cabinets.
The cost to install each cabinet is $45. Since there are n cabinets, the total cost for installation would be $45 multiplied by the number of cabinets, or n * $45.
Therefore, the total cost for a set of n cabinets would be the cost of delivery plus the cost of installation:
Total Cost = $150 (Delivery) + n * $45 (Installation)
Total Cost = $150 + $45n
b) To find the total cost for a set of 18 cabinets, we can substitute n = 18 into the formula we derived in part a:
Total Cost = $150 + $45 * 18
Total Cost = $150 + $810
Total Cost = $960
Therefore, the total cost for a set of 18 cabinets is $960.
c) To find the number of cabinets if the total cost was $735, we can rearrange the formula from part a and solve for n:
Total Cost = $150 + $45n
$735 = $150 + $45n
Subtracting $150 from both sides:
$735 - $150 = $45n
$585 = $45n
Dividing both sides by $45:
$n = \frac{585}{45}$
$n = 13$
Therefore, the number of cabinets if the total cost was $735 is 13.
(2nd Question)
a) To find the total cost of playing tennis for h hours at this club in a year, we need to consider the annual membership cost plus the cost for each hour of court time.
The annual membership cost is $600. This is a fixed cost and does not depend on the number of hours played.
The cost for each hour of court time is $15. Since there are h hours, the total cost for court time would be $15 multiplied by the number of hours, or $15h.
Therefore, the total cost of playing tennis for h hours in a year would be the membership cost plus the cost for court time:
Total Cost = $600 (Membership) + $15h (Court Time)
b) To find the total cost of playing tennis for a specific number of hours, let's say 50 hours, we can substitute h = 50 into the formula we derived in part a:
Total Cost = $600 + $15 * 50
Total Cost = $600 + $750
Total Cost = $1350
Therefore, the total cost of playing tennis for 50 hours in a year would be $1350.
(3rd Question)
a) To compute the total cost of renting a car for one day and driving it for m miles, we need to consider the daily rental cost plus the cost per mile.
The daily rental cost is $30. This is a fixed cost and does not depend on the number of miles driven.
The cost per mile is $0.25. Since there are m miles, the total cost for mileage would be $0.25 multiplied by the number of miles, or $0.25m.
Therefore, the total cost of renting a car for one day and driving it for m miles would be the daily rental cost plus the cost per mile:
Total Cost = $30 (Daily Rental) + $0.25m (Mileage Cost)