The Johnsons need a new living room couch. The couch they like costs $2,700. The salesperson told the Johnsons that the couch will be on sale next month for 20% off.

If the sales tax rate in their city is 7.5%, how much will the Johnsons save including sales tax, if they wait until the couch goes on sale?

Question

The Johnsons need a new living room couch. The couch they like costs $2,700. The salesperson told the Johnsons that the couch will be on sale next month for 20% off.

If the sales tax rate in their city is 7.5%, how much will the Johnsons save including sales tax, if they wait until the couch goes on sale?

anonymous · Answer

@jim_thompson5910 help pls!

anonymous · Answer

Savings = Price if they pay now - Price if they wait
            = 1.075 * 2700         -  1.075 * (0.8 * 2700)

anonymous · Answer

You can add on a 7.5% sales tax by just multiplying by 1.075
To reduce something by 20%, just multiply it by (1 - 0.2) or 0.8

anonymous · Answer

wait what im confused @Mertsj

mertsj · Answer

Would you agree that right now they have to pay 100% of 2700 plus the sales tax?

anonymous · Answer

yes @Mertsj

anonymous · Answer

= 1.075 * 2700         -  1.075 * (0.8 * 2700)
= $580.50

mertsj · Answer

So since the sales tax is 7.5%, right now they have to pay 107.5 percent of 2700 or 1.075(2700) which is $2902.50

anonymous · Answer

attachment

anonymous · Answer

is it D

mertsj · Answer

Next month the couch is 20% off which means they DON'T have to pay 20%, which means they DO have to pay 80%

anonymous · Answer

Yes. And the amount they pay if they wait is 1.075 times (80% of 2700)
which is 0.86 * 2700 = 2322

mertsj · Answer

No it is not D .  The question asks how much will they SAVE?

anonymous · Answer

It's C...just as I calculated above

jim_thompson5910 · Answer

If you do not wait for the sale, then you simply pay the $2,700 plus 7.5% of that (add on the sales tax)


2700 + 0.075*2700 = 2,902.50


So if you don't wait for the sale, then you pay a total of $2,902.50 


----------------------------------------------------------------------------


Now let's say you wait for the sale of 20% off


20% of $2,700 = (20/100)*2700


20% of $2,700 = 0.20*2700


20% of $2,700 = 540


Taking 20% off of $2,700 means you subtract off $540


2700 - 540 = 2160


Now add on 7.5% sales tax


2160 + 0.075*2160 = 2322


So you will pay $2,322 if you wait next month for the 20% off sale.

----------------------------------------------------------------------------


The difference in those final prices is:  2902.50 - 2322 = $580.50

anonymous · Answer

Thx i got it! @jim_thompson5910

anonymous · Answer

And all of that can be simplified to
Savings = Price if they pay now - Price if they wait
            = 1.075 * 2700         -  1.075 * (0.8 * 2700) = 580.5