SOLUTION: I don't know how to write an equation for this: Shirley is going to have the exterior of her home painted. Tim's Painting charges $250 plus $14 an hour. Colorful Paints charges $22

Question 1045730: I don't know how to write an equation for this: Shirley is going to have the exterior of her home painted. Tim's Painting charges $250 plus $14 an hour. Colorful Paints charges $22 per hour. How many hours would the job need to take for Tim's Painting to be the better deal?
I'm pretty sure the answer is 32 hours. I just don't know how to write an equation showing my answer.
There is another 1 that I don't know how to do at all.
Tracey is looking at different travel agencies to plan her vacation. ABC Travel offers a plane ticket for $295 and a rental car for $39 per day. M&N Travel offers a plane ticket for $350 and a rental car for $33 per day. What is the minimum number of days that Shirley's vacation should be for M&N Travel to have the better deal?
I have no idea how to answer this or write the equation.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Shirley is going to have the exterior of her home painted.
Tim's Painting charges $250 plus $14 an hour.
Colorful Paints charges $22 per hour.
How many hours would the job need to take for Tim's Painting to be the better deal?
:
write a cost equation for each, t = time in hrs
Tims: C(t) = 14t + 250
Colorful: C(t) = 22t
:
Colorful's cost is greater than Tim's cost
22t > 14t + 250
22t - 14t > 250
8t > 250
t > 250/8
t > 31.25; your answer of 32 hrs is correct. Prove this:
22*32 = $704, Colorful
14*32 + 250 = $698, Tim's
:
:
This is much the same thing
Tracey is looking at different travel agencies to plan her vacation.
ABC Travel offers a plane ticket for $295 and a rental car for $39 per day.
M&N Travel offers a plane ticket for $350 and a rental car for $33 per day.
What is the minimum number of days that Shirley's vacation should be for M&N Travel to have the better deal?
let d = no. of days
ABC: C(d) = 39d + 295
M%N: C(d) = 33d + 350
:
ABC cost is greater than M&N cost
39d + 295 > 33d + 350
39d - 33d > 350 - 295
6d > 55
d > 55/6
d > 9.16 ~ 10 days M&N will be the better deal
:
Prove this
ABC: 39(10) + 295 = $685
M%N: 33(10) + 350 = $680
:
:
Does this make sense to you now? Not really that hard, is it? CK
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