An Internet company charges a one-time setup fee of $44.99 and a monthly fee of $29.99 for Internet service. The company is offering a 25% discount on the monthly fee for the first year.

Part A
Write an expression the determine the cost, after the discount and before tax, of "m" months of service during the first year.

Part B
An 8% sales tax is added to the total cost. Rewrite the expression in Part A to include the sales tax.

Question

An Internet company charges a one-time setup fee of $44.99 and a monthly fee of $29.99 for Internet service. The company is offering a 25% discount on the monthly fee for the first year.

Part A
Write an expression the determine the cost, after the discount and before tax, of "m" months of service during the first year. 

Part B
An 8% sales tax is added to the total cost. Rewrite the expression in Part A to include the sales tax.

calculusxy · Answer

@perl

solomonzelman · Answer

alright, lets see. What have you got so far ?

calculusxy · Answer

For part A I got the expression:
$44.99 + ($29.99m - ($29.99 x 0.25))

solomonzelman · Answer

so you are subtracting 25%, but couldn't you write this better a bit?

calculusxy · Answer

That is the part where I am getting confused at.

solomonzelman · Answer

What I mean is that you are subtracting 25% (from 100%)

So instead of
$44.99 + ($29.99m - ($29.99 x 0.25)) 
you will say
$44.99 + 0.75($29.99m)) 

(because by subtracting 25%, you are taking 100% of the whole thing)

calculusxy · Answer

Oh. I get it now.

calculusxy · Answer

Can you help me with Part B?

solomonzelman · Answer

sure, what do you have for part A?

solomonzelman · Answer

Whatever that is that you have for part A (which is the total cost) you are adding 8% to that.

When you add 8% to something you are taking 108% of it.
Taking 108% is as you know, the same as multiplying times 1.08.

solomonzelman · Answer

hope I am making sense:)

calculusxy · Answer

How would I add it to the expression, to get the sales tax?

solomonzelman · Answer

well, you have an expression for part A (whatever you get) that is the TOTAL cost.

You are adding 8% to this TOTAL cost, which means that with tax you are paying (100+8)% of the cost.
100% of the cost is what you have for part A, and additional 8% of the cost is the tax.

NOW, taking (100+8)% of the TOTAL cost, is same as multiplying this TOTAL cost by 1.08
(because when you convert percent to decimals)

calculusxy · Answer

So if I just multiply 1.08 to the total expression from Part A, then that it will add the expression to the total cost.

calculusxy · Answer

@SolomonZelman

solomonzelman · Answer

yes

multiplying that expression in part A, will get you the TOTAL cost including the tax

calculusxy · Answer

Okay thank you. Can you help me with another question?  I will make a new post.

solomonzelman · Answer

I will try my best, if I can:)

perl · Answer

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