Emma is planning her summer and would like to work enough to travel and buy a new laptop.

She can earn $90 each day, after deductions, and she can work a maximum of 40 days in July and

August, combined. She expects each day of travel will cost her $150 and the laptop she hopes to

buy costs $700.

a) Write a linear equation that represents the number of days Emma can work and travel and

still earn enough for her laptop.

b) Sketch the graph of this relation.

c) State the domain and range of this relation.

d) If Emma plans to travel for 6 days, how many days does she need to work?

For the answer to the question above, f x is the number of days she works, she'll earn $90x

After buying the laptop, she'll have $90x - $700 left over, which will pay for ($90x - $700) / $150 days of travel. So we have y = ($90x - $700) / $150 = (9x - 70) / 15 = 0.6x - (14/3)

Note that y can't be negative. Also, if y = 0, then Emma doesn't get to travel at all, so we should avoid that. So we have:

0.6x - (14/3) > 0

0.6x > 14/3

x > (14/3) / 0.6

x > 70/9

The question says that x can be up to 40, so the domain is 70/9 < x < = 40

That's approximately 7.777 ... < x < = 40

Multiply those numbers by 0.6 and then subtract 700 to get the range:

0 < y < = 58/3

That's approximately 0 < y < = 19.333