Mathematics High School

you pay a processing fee and a daily fee to rent a beach house. the table shows the total cost of renting the beach house for different numbers of days.

a) what is the processing fee? the daily fee?

b) you can spend no more than $1200 on the beach house rental. what is the maximum number of days you can rent the beach house?

Answers

Answer 1

Answer:

a) The daily fee is $102

The processing fee is $42

b) The maximum number of days the beach house can be rented with no more than $1,200 is (by rounding down) 11 days

Step-by-step explanation:

The data given in the table are as follows;

Number of days (t) [tex]{}[/tex] Total cost, T (dollars)

2 [tex]{}[/tex] 246

4 [tex]{}[/tex] 450

6 [tex]{}[/tex] 654

8 [tex]{}[/tex] 858

Whereby, we have that the processing fee is P, and the daily fee is D, we can write;

Total cost, T = D × t + P

From the table, we have;

When t = 2 days and T = $246, the above equation for total cost becomes;

$246 = D × 2 + P = 2·D + P

246 = 2·D + P.....(1)

Similarly, when t = 6 days, and T = $654, we have;

$654 = D × 6 + P = 6·D + P

654 = 6·D + P.....(2)

Subtracting equation (1) from equation (2) gives;

654 - 246 = 6·D + P - (2·D + P)

408 = 4·D

D = 408/4 = 102

The daily fee, D = $102

From equation (1), we have;

246 = 2·D + P = 2 × 102 + p

p = 246 - 2 × 102 = 42

P = $42

The processing fee, P = $42

b) Given that the maximum amount available (total amount) for spending on the beach house rental = $1200, we have;

T = D × t + P

Where, D = $102 and P = $42 are constants and T = $1,200, we have;

1,200 = 102 × t + 42

t = (1200 - 42)/102 ≈ 11.35 days

Given that we can only rent the beach house for a whole number of days, the number of days the beach house can be rented is therefore, by rounding down, t = 11 days.

Answer 2

a) D = $102

P = $42

b) t = 11 days

Step-by-step explanation:

Given :

Data in the table -

Days (t) Total cost (dollors) (T)

2 246

4 450

6 654

8 858

Calculation :

a) Let the total processing fee is P and the daily fee is D.Now,

[tex]\rm T = D \times t + P[/tex] ------------ (1)

Now, from the table we have ,

When t = 2 days and T = $246 than equation (1) becomes

[tex]\rm 246 = D\times 2+ P = 2D + P[/tex]

246 = 2D + P ------- (2)

Similarly, when t = 6 days, and T = $654, then equation (1) becomes

[tex]\rm 654 = D\times 6+ P = 6D + P[/tex]

654 = 6D + P --------- (3)

Subtracting equation (2) from equation (3) ,

654 - 246 = 6D + P - (2·D + P)

408 = 4D

D = $102

From equation (2),

246 = 2·D + P = 2 × 102 + p

p = 246 - 2 × 102 = 42

P = $42

b) Given:

The maximum amount available for spending on the beach house rental = $1200

Now,

[tex]\rm T= D\times t + P[/tex]

Where, D = $102 and P = $42 are constants and T = $1,200,

1200 = 102t + 42

t = 11.35 days

Given that we can only rent the beach house for a whole number of days. therefore, the number of days the beach house can be rented is, t = 11 days.

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