chapter 6_the rest

100

A taxi charges a fixed fee of $5 plus $2 per kilometre.

Write an equation for the total cost CC of a trip of dd kilometres.
What will a 12-km trip cost?

C=2d+5

For 12 km:

C=2(12)+5=$29

200

Clue: A concert venue sells tickets for $15 each and charges a one-time service fee of $8.

Write an equation for the total cost C for n tickets.
How much will 6 tickets cost?
Is this a direct or partial variation?

Answer:

C=15n+8

C=15(6)+8=$98

Partial variation.

300

Two bicycle rental companies have different pricing plans.

Company A: $20 starting fee + $4 per hour
Company B: $8 starting fee + $6 per hour

Write an equation for each company.
After how many hours will the two companies charge the same amount?
What will that cost be?

Answer:

A=4h+20

B=6h+8

Set them equal:

4h+20=6h+8 h=6

Cost: 4(6)+20=$44

Intersection: (6,44)

300

Find the equation of the line perpendicular to

4x−y=8

that has the same y-intercept as the line

y=21x−6.

Slope: m=4

Perpendicular slope: -1/4

Same y-intercept: b=−6

y=−1/4(x)−6

300

Find the equation of the line perpendicular to

5x−2y=10

that has a y-intercept of 4.

y=-2/5(x)+4

2x+5y=20

300

Parallel

Find the equation of the line parallel to

3x−4y=12

that has the same yy-intercept as

y=2x+5.

y=3/4(x)+5

400

Two swimming pools charge different fees.

Pool A: $50 membership fee plus $5 per visit
Pool B: $20 membership fee plus $8 per visit

At how many visits will the total costs be equal? Which pool is cheaper if a student visits fewer times than the break-even point?

Answer:

50+5v=20+8v

30=3v

v=10

Cost:

50+5(10)=$100

Intersection: (10,100)

For fewer than 10 visits, Pool B is cheaper.

400

Find the equation of the line perpendicular to

4x+3y−12=0

that passes through (−2,5).

Rewrite the given line:

3y=−4x+12

y=−4/3x+4

Perpendicular slope: m=3/4

Using (−2,5), b=13/2

Therefore: y=3/4x+13/2

or in standard form: 3x−4y=−26

400

Find the equation of the line parallel to

2x+5y=15

that passes through (5,−1).

m=−2/5

b=1

y=-2/5(x)+1

400

Find the equation of the line perpendicular to

2x+5y=15

that has the same y-intercept as the line

y=−3x+4.

Perpendicular slope: m=5/2

Same y-intercept: b=4

y=5/2(x)+4

500

Two cell phone plans are available:

Plan A: $60 per month with unlimited texts
Plan B: $20 per month plus $0.10 per text

Write an equation for each plan.
How many texts make the plans cost the same?
What is the monthly cost at that point?
Which plan is better for someone who sends more texts?

Answer:

A=60

B=20+0.10t

Set equal:

60=20+0.10t

40=0.10t

t=400

Cost: $60

For more than 400 texts, Plan A is better.

500

A car rental company offers two plans:

Plan A: $80 per day plus $0.30 per kilometre
Plan B: $50 per day plus $0.50 per kilometre

Write an equation for each plan.
Find the distance at which the two plans cost the same.
Find the cost at that distance.
Which plan is better for a trip of 100 km?
Which plan is better for a trip of 300 km?

Answer:

A=80+0.30d

B=50+0.50d

A=B then d=150 km

Cost:

80+0.30(150)=$125

At 100 km → Plan B is cheaper.

At 300 km → Plan A is cheaper.

500

A school is choosing between two companies to print T-shirts.

Company A: $100 setup fee + $8 per shirt
Company B: $40 setup fee + $10 per shirt

Clue:

The school wants to know when both companies will cost the same.

Write a system of equations.
Solve the system.
State the intersection point.
Explain which company is better for fewer shirts and which is better for more shirts.

Answer:

A=100+8x

B=40+10x

Set equal:

100+8x=40+10x 60=2x x=30

Cost: 100+8(30)=340

Final Answer: (30, 340)

The companies charge the same amount for 30 shirts, at a cost of $340.

Fewer than 30 shirts → Company B
More than 30 shirts → Company A

500

Find the equation of the line perpendicular to

3x−4y=12

that has the same y-intercept as the line

y=2x+5.

m=-4/3

Same y-intercept as y=2x+5: b=5

y=−4/3(x)+5