Solve the following equations with rational coefficients .

Mr. Martin and his son are planning a fishing trip to Alaska. The rates of two companies are shown.

Mumz [18]

Answer:

Part A) Fisherman's Service will provide a better deal for a three days trip as it will cost $480 compare to the Wild Fishing Inc.'s deal that costs around 550$

Part B) Wild Fishing's Inc. would charge $700 for 6 days for both of them.

Part C) Let w be expression for Wild Fishing Inc. to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.

w = 2(200) + 2n(25) = 400 + 50n

Let f be expression for Fisherman's Service to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.

f = 2(150) + 2n(30) = 300 + 60n

Step-by-step explanation:

Part (A) Which company offers a better deal for a three day trip for Mr. Martin and his son? What will be the cost?

The rate offered by Wild Fishing Inc:

Round Trip Flight $200 / Daily Rate $25

The rate offered by Fisherman's Service:

Round Trip Flight $150 / Daily Rate $30

Analyzing Wild Fishing Inc. Offer for a three day trip

As Mr. Martin and his son are planning a fishing trip to Alaska.

Expenses cost for Mr. Martin and his son if they chose Wild Fishing Inc

The formula to calculate Mr Martin expenses for 3 day trip:

Round trip Cost + 3 (Daily rate) ⇒ 200 + 3 (25) = $275.......[A]

The formula to calculate Mr Martin's son expenses for 3 day trip:

Round trip Cost + 3 (Daily rate) ⇒ 200 + 3 (25) = $275.......[B]

Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Wild Fishing Inc. deal:

Net expense faced by Mr. Martin and his son: 275 + 275 = 550$

So, Wild Fishing Inc. will cost 550$ to both Mr. Martin and his son.

Analyzing Fisherman's Service Offer for a three day trip

As Mr. Martin and his son are planning a fishing trip to Alaska.

Expenses cost for Mr. Martin and his son if they chose Fisherman's Service

The formula to calculate Mr Martin expenses for 3 day trip:

Round trip Cost + 3 (Daily rate) ⇒ 150 + 3 (30) = $240.......[A]

The formula to calculate Mr Martin's son expenses for 3 day trip:

Round trip Cost + 3 (Daily rate) ⇒ 150 + 3 (30) = $240.......[B]

Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Fisherman's Service deal:

Net expense faced by Mr. Martin and his son: 240 + 240 = 480$

So, Fisherman's Service will cost 480$ to both Mr. Martin and his son.

Choosing the right company that offers a better 3 days deal:

As we have determined that

Wild Fishing Inc. will cost 550$ to both Mr. Martin and his son.
Fisherman's Service will cost 480$ to both Mr. Martin and his son.

Therefore, Fisherman's Service will provide a better deal for a three days trip as it will cost $480 compare to the Wild Fishing Inc.'s deal that costs around 550$.

Part (B) Which company would charge $700 for 6 days for both of them?

Checking Wild Fishing Inc. expenses for 6 days trip:

The formula to calculate Mr Martin expenses for 6 day trip:

Round trip Cost + 6 (Daily rate) ⇒ 200 + 6 (25) = $350.......[A]

The formula to calculate Mr Martin's son expenses for 3 day trip:

Round trip Cost + 6 (Daily rate) ⇒ 200 + 6 (25) = $350.......[B]

Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Wild Fishing Inc. deal for 6 days:

Net expense faced by Mr. Martin and his son: $350 + $350 = 700$

Checking Fisherman's expenses for 6 days trip:

The formula to calculate Mr Martin expenses for 6 day trip:

Round trip Cost + 6 (Daily rate) ⇒ 150 + 6 (30) = $330.......[A]

The formula to calculate Mr Martin's son expenses for 3 day trip:

Round trip Cost + 6 (Daily rate) ⇒ 150 + 6 (30) = $330.......[B]

Adding Equation [A] and [B] will bring the net expense faced by Mr. Martin and his son if they chose to get Fisherman's Service deal for 6 days:

Net expense faced by Mr. Martin and his son: $330 + $330 = 680$

So, Wild Fishing's Inc. would charge $700 for 6 days for both of them.

Part (C) Write an expression to represent the cost of the trip for Mr. Martin and his son for each company.

Expression for Wild Inc.

Let w be expression for Wild Fishing Inc. to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.

w = 2 (Round trip Cost) + 2n (Daily rate)

As Round trip costs $200 and $25 is the daily rate for Wild Fishing Inc.

So, w can be written as:

w = 2(200) + 2n(25) = 400 + 50n

Expression for Wild Inc.

Let f be expression for Fisherman's Service to represent the cost of the trip for both Mr. Martin and his son for n number of days trip.

f = 2 (Round trip Cost) + 2n (Daily rate)

As Round trip costs $150 and $30 is the daily rate for Fisherma''s Service.

So, w can be written as:

f = 2(150) + 2n(30) = 300 + 60n

Keywords: cost, expenses, deal

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8 0

3 years ago

Find a polynomial function whose graph passes through(-1,-1)(0,7)(1,9)(2,17)

frez [133]

Answer:

The required polynomial is f(x)= $2x^{3}-3x^{2}+3x+7$

Step-by-step explanation:

Given that polynomial is passing through points (-1,-1) (0,7) ( 1,9) and (2,17)

Let, The required polynomial be f(x)= $ax^{3}+bx^{2}+cx+d$

For point (-1,-1)

f(x)= $ax^{3}+bx^{2}+cx+d$

f(-1)= $a(-1)^{3}+b(-1)^{2}+c(-1)+d$

(-1)a+b-c+d=(-1) Equation 1

For point (0,7)

f(x)= $ax^{3}+bx^{2}+cx+d$

f(0)= $a(0)^{3}+b(0)^{2}+c(0)+d$

d=7 Equation 2

For point ( 1,9)

f(x)= $ax^{3}+bx^{2}+cx+d$

f(1)= $a(1)^{3}+b(1)^{2}+c(1)+d$

a+b+c+d=9 Equation 3

For point (2,17)

f(x)= $ax^{3}+bx^{2}+cx+d$

f(2)= $a(2)^{3}+b(2)^{2}+c(2)+d$

8a+4b+2c+d=17 Equation 4

Replacing value of d of equation 2 in equation 1,3,4

For equation 1:

(-1)a+b-c+d=(-1)

(-1)a+b-c=(-8)

For equation 3:

a+b+c+d=9

a+b+c=2

For equation 4:

8a+4b+2c+d=17

8a+4b+2c=10

Now,

On adding equation 1 and 3

For equation 1: (-1)a+b-c=(-8)

For equation 3: a+b+c=2

((-1)a+b-c)+(a+b+c)=(-8)+2

2b=(-6)

b=(-3)

Replacing value of b in equation 1 and 4:

For equation 1: (-1)a+b-c=(-8)

(-1)a+(-3)-c=(-8)

(-1)a-c=(-5) Equation 4

For equation 4: 8a+4b+2c=10

8a+4b+2c=10

8a+4(-3)+2c=10

8a+2c=22 Equation 5

For value of a and c:

Equation 4 can be write as

(-1)a-c=(-5)

a+c=5

a=5-c

Replacing value of a in equation 5

8a+2c=22

8(5-c)+2c=22

40-8c+2c=22

-6c=-18

c=3

So,

a=5-c=5-3=2

a=2

Thus,

The value of

a=2, b=(-3), c=3 and d=7

The required polynomial is

f(x)= $ax^{3}+bx^{2}+cx+d$

f(x)= $2x^{3}-3x^{2}+3x+7$

5 0

3 years ago

The sum of 3 consecutive odd integers is -15. Find the integers.

Aleonysh [2.5K]

Answer:

-7, -5, -3

Step-by-step explanation:

they equal to -15 together

6 0

3 years ago

If you were to graph 1.14, 1.15, and 0.5. what would you count by on your number line?

GREYUIT [131]

If you want to include 0, the overall interval is 115 times 0.01, or 23 times 0.05 or 11.5 times 0.10. The latter might make it harder to plot 1.14, so I'd probably use an interval of 0.05.

Between 6 or 7 and about 25 intervals on a graph's scale are about right. More makes it pretty busy and sometimes difficult to tell which mark is associated with the number. A fewer number is indicated only if there are a fewer number of discrete values that need to be shown to adequately identify the data points.

6 0

3 years ago

In a fruit survey, children choose their favorite fruit out of apples, bananas and watermelon. 29% chose apples, 41% chose banan

Alex73 [517]

Answer: 30% chose watermelons.

Step-by-step explanation:

if 29% chose apples and 41% chose bananas, that equals 70%

So, out of 100%, 70% chose both apples and bananas, which leaves 30% for watermelons.

8 0

3 years ago

Solve the following equations with rational coefficients￼ .

Solve the following equations with rational coefficients .