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Equations,money problems, graphs-help please

0 votes

Before hiring a car for a day trip, Kyle called several car hire services for some quotes.

Company:                         Cost Per day:

Sam’s Car Hire                  $25, plus $0.07 (7 cents) for each km.

Fleet Car Hire                    $50 for each day.

Daytripper’s Car Hire        $35, plus $0.05 (5 cents) for each km.

1.       Set yp a table of values for each car hire firm showing trips from 0km to 450km in 50km increments.

 

Let K stand for number of kilometres travelled

Let Cs stand for Sam’s hire cost

Let Cf stand for Fleet hire cost

Let Cd stand for Daytripper’s hire cost

 

a)      For each company write an equation for the cost.

b)      Plot three equations on the same graph.

Let the x axis have the distance with values from 0 to 600km, and the y axis show the cost C with values from 0 to $80.

c)       Explain which deal is better for

(i)                  Short trips ?

(ii)                Long trips?

Sometimes it makes no difference which company you use.

d)      For what distances does:

(i)                  Cs=Cf?

(ii)                Cf=Cd?

(iii)               Cs=Cd?

 

                   2.    For the design below: 

                    http://www.flickr.com/photos/99973477@N03/11444159853/

a)      Draw the next three shapes in the sequence.

b)      Draw up a table for the first ten shapes in the sequence, and the number of matches required to complete the shape.

c)       Determine the word relationship for the sequence of outputs.

d)      Determine the formula which would allow you to find the number of matches in any shape in the sequence.

e)      Draw a graph of the relationship.

 

3.       For the design below:

                         http://www.flickr.com/photos/99973477@N03/11444055415/

a)      Draw the next three shapes in the sequence.

b)      Draw up a table for the first ten shapes in the sequence, and the number of matches required to complete the shape.

c)       Determine the word relationship for the sequence of outputs.

d)      Determine the formula which would allow you to find the number of matches in any shape in the sequence.

e)      Draw a graph of the relationship.

 

4. A student banks $200 when she starts secondary College in Grade 7. In Grade 8 she banks $250,$300 in Grade 9, and so on. She is at school for 6 years.

a)  Determine a formula relating the amount deposited during a year (200,250,...) to how many years they have been saving(1,2,...).

Because the deposits are increasing, the formula for the bank balance is more complex and is not a linear relationship. Answer the following using a table.

b)  What is the total amount she has banked by the time she finishes after 6 years?

c)   If she continued banking in this manner after she leaves school, how many years(from the start) will it take for her balance to exceed $15,000?

 

asked Dec 19, 2013 in BASIC MATH by Lobo142 Rookie

10 Answers

0 votes

1) kyle called several car hire services

k

Cs

Cf

Cd

0

25

50

35

50

28.5

50

37.5

100

32

50

40

150

35.5

50

42.5

200

39

50

45
250 42.5 50 47.5
350 46 50 50
400 49.5 50 52.5
450 53 50 55

a)Equation for the each company for the cost

Cs cost is y = 25+0.07x

Cf cost is y = 50

Cd cost is y = 35+0.05x

answered Dec 23, 2013 by dozey Mentor

Above solution (1) is wrong.

See the correct solution below.

0 votes

b) Three equations on same graph.

Draw the coordinate plane.

Let the x axis have the distance with values from 0 to 600km and the y axis show the cost C with values from 0 to $80.

From the  equations.

 y = 25+0.07x

 y = 50

 y = 35+0.05x

answered Dec 23, 2013 by dozey Mentor
0 votes

c) Sam’s Car Hire company deal is better for short trips, why because Compare to other two companies

From 0 to 350 km price is lowest.

Fleet Car Hire company deal is better for long tripes, why because compare to other two companies 

it is maintain standard price to short or long distance . It's cost only $50 for each day.

answered Dec 23, 2013 by dozey Mentor
0 votes

1) kyle called several car hire services

k

Cs

Cf

Cd

0

25

50

35

50

28.5

50

37.5

100

32

50

40

150

35.5

50

42.5

200

39

50

45
250 42.5 50 47.5
300 46 50 50
350 49.5 50 52.5
400 53 50 55
450 56.5 50 57.5
answered Dec 23, 2013 by dozey Mentor
0 votes

a)Equation for the each company for the cost

Cs cost is y = 25+0.07x

Cf cost is y = 50

Cd cost is y = 35+0.05x

answered Dec 23, 2013 by dozey Mentor
0 votes

C) Sometimes it makes no difference i prefer fleet car hire company because i think it gives comfortable journey compare remaining company cars.

d) (i) when 350 km, Cs cost is 49.5 and Cf cost is 50,it seems to be equal.(approximately)

(ii) when distance is 300 km, Cf equals to Cd.

Cost is 50.

(iii) When distance is 500 km, Cs equls to Cd.

Cost is 60

answered Dec 23, 2013 by dozey Mentor
0 votes

(3).(a).

 

(b). Make the table

Numbers

1

2

3

4

5

6

7

8

9

10

Number of shapes

1

4

7

10

13

16

19

22

25

28

 

(c). The word relationship for the sequence of outputs :

Number of shapes = The difference between three times a number(n) and two.

 

(d). Determine the formula which would allow you to find the number of matches in any shape in the sequence.

Sequence : 1, 4, 7, 10, . . . . . . .nth term.

Since common difference is 3, the above sequence is arithmetic sequence.

nth term tn = a1 + (n - 1)d, where a1 = first term and d = common term.

tn = 1 + (n - 1)3

tn = 1 + 3n - 3

tn = 3n - 2.

 

(e). Draw a graph of the relationship y = 3x - 2.

 

answered Aug 21, 2014 by casacop Expert
0 votes

(2).(a). The next three shapes in the sequence :

 

(b). Make the table

Numbers

1

2

3

4

5

6

7

8

9

10

Number of shapes

1

2

3

4

5

6

7

8

9

10

 

(c). The word relationship for the sequence of outputs :

Number of shapes = number(n).

 

(d). Determine the formula which would allow you to find the number of matches in any shape in the sequence.

Sequence : 1, 2, 3, 4, . . . . . . .n.

Since common difference is 1, the above sequence is arithmetic sequence.

nth term tn = a1 + (n - 1)d, where a1 = first term and d = common term.

tn = 1 + (n - 1)1

tn = 1 + n - 1

tn = n.

 

(e). Draw a graph of the relationship y = x.

 

answered Aug 21, 2014 by casacop Expert
0 votes

(4).(a).

Year                     Balance after each compoundig.

  0                        200                            [P = P]

  1                        200 + 250 = 450        [P1 = P + Pr = P(1 + r)]

  2                        450 + 300 = 750        [P2 = P1(1 + r) = P(1 + r)(1 + r) = P(1 + r)2]

  3                        750 + 350 = 1100      [P3 = P2(1 + r) = P(1 + r)2(1 + r) = P(1 + r)3]

  .                        .                                             .

  .                        .                                             .

  .                        .                                             .

  t                        .                                [Pt = P(1 + r)t]

For n compounings per year : A = P(1 + r/n)nt, where P = principal, r = interest rate(in decimal form), t = number of years.

For continuous compouning : A = Pert.

 

(b). The total amount after 6 years :

Here find the r value :

If A = 450, P = 200 and t = 1 then 450 = 200e(1)r    ------> (1).

If A = 750, P = 200 and t = 2 then 750 = 200e(2)r    ------> (2).

Divide the equation 2 by equation 1.

750/450 = 200e2r / 200er -----> er = 1.67  -----> r = ln 1.67 = 0.5.

The total amount after 6 years A = (200)e(0.5)(6) = 200 * 20.0855 = 4017.107 dollars.

 

(C). Find the time in years :

A = 15, 000 dollars and r = 0.5, P = 200.

A = Pert.

15,000 = (200)e(0.5)(t)

75 = et/2 =

ln 75 = t/2

8.635 years = t.

answered Aug 21, 2014 by casacop Expert
0 votes

(1). Make the table :

k

Cs = 25 + 0.07k

Cf = 50

Cd = 35 + 0.05k

0

Cs = 25 + 0.07(0) = 0

50

Cd = 35 + 0.05(0) = 35

50

Cs = 25 + 0.07(50) = 28.5

50

Cd = 35 + 0.05(50) = 37.5

100

Cs = 25 + 0.07(100) = 32

50

Cd = 35 + 0.05(100) = 40

150

Cs = 25 + 0.07(150) = 35.5

50

Cd = 35 + 0.05(150) = 42.5

200

Cs = 25 + 0.07(200) = 39

50

Cd = 35 + 0.05(200) = 45

250

Cs = 25 + 0.07(250) = 42.5

50

Cd = 35 + 0.05(250) = 47.5

300

Cs = 25 + 0.07(300) = 46

50

Cd = 35 + 0.05(300) = 50

350

Cs = 25 + 0.07(350) = 49.5

50

Cd = 35 + 0.05(350) = 52.5

400

Cs = 25 + 0.07(400) = 53

50

Cd = 35 + 0.05(400) = 55

450

Cs = 25 + 0.07(450) = 56.5

50

Cd = 35 + 0.05(450) = 57.5

 

(a).

Company name                          Equation for the cost

Sam’s Car Hire                           Cs = 25 + 0.07k

Fleet Car Hire                             Cf = 50

Daytripper’s Car Hire                  Cd = 35 + 0.05k.

 

(b). Plot three equations on the same graph.

 

 

C).

(i). From the graph, Sam’s Car Hire company deals is better for Short trips.

(ii). From the graph, Fleet Car Hire company deals is better for Long trips.

 

(d).

(i). Cs = Cf

⇒ 25 + 0.07k = 50

⇒ 0.07k = 25

⇒ k = 357.143 km.

 

(ii). Cf = Cd

⇒ 50 = 35 + 0.05k

⇒ 15 = 0.05k

⇒ k = 300 km

 

(iii). Cs = Cd Cf = 50 Cd = 35 + 0.05k.

⇒ 25 + 0.07k = 35 + 0.05k

⇒ 0.02k = 10

⇒ k = 500 km.

answered Aug 21, 2014 by casacop Expert

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