Question

Julie gets a pre-paid cell phone. Initially she has $40 balance on the phone. She talked to her mom for 5 minutes and her balance is now $39.25. She talked to her sister for 30 minutes and her balance is now $34.75. What will her balance be after she has talked for 75 minutes? A painter is going to charge $90 for paint. Painting your bedroom takes 1 hour and costs $125. Painting your kitchen takes 4 hours and costs $230. How much will it cost to paint the outside of your house if it will take 10 hours?
Which problem is linear? And show the equation table slope calculation after you figured out which problem is linear

Answer 1

The relationship between the balance in the phone and the number of  

minutes of talking is a linear relationship.

• Her balance after talking for 75 minutes is $28.75

• The cost to paint the outside of the house is $350

Reasons:

First question

Initial balance in Julie's phone = $40

The balance after talking for 5 minutes = $39.25

Her balance after talking for 30 minutes = $34.75

Required:

Her balance after she has talked for 75 minutes

Solution:

$The \ rate \ of \ change \ of \ her \ balance =\dfrac{34.75 - 39.25}{35 - 5 } = -0.15$

Therefore, the rate of change of her balance with time = -0.15 Dollars/minute

The equation for her balance is; y - 39.25 = -0.15 × (x - 5)

y = -0.15·x + 0.75 + 39.25 = -0.15·x + 40

y = 40 - 0.15·x

When x = 75, y = 40 - 0.15×75 = 28.75

• Her balance after talking for 75 minutes = $28.75

Second question:

The amount charged for paint = $90

Number of hours to paint the bedroom = 1 hour

Cost to paint the bedroom = $125

Number of hours to paint the kitchen = 4 hour

Cost to paint the kitchen  = $230

The cost to paint per hour is therefore;

$Cost \ per \ hour =\dfrac{230- 125}{4 - 1 } = 35$

The cost to paint per hour = $35 /hour

• The cost to paint the outside for 10 hours = 10 × $35 = $350

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