00:02: Let's take a look at a problem that involves both a discount and sales tax. So what we're asked is to find the price you must pay for a $40 sweater that is being discounted for 25% off and for which the sales tax is 6%. So in order to find the actual sale price of the sweater, we have to figure out what the discounted price is going to be. So it's gonna be 25% off. So the two ways we can do it... The maybe most obvious way is just to first figure out what is 25% of the sweater price. So what is 25% of 40? And to do that, of course, we just convert the 25% into a decimal which is 0.25, convert the "of" to a multiplication since that's usually what it represents, and then do the math. If we multiply 0.25 times 40, we will get 10. So 10 is the 25% that's going to be discounted. So we have to subtract that from the actual price. So 40 minus 10 is obviously $30. So $30 would be the price. 01:20: Now, another way you could do that same calculation is to think, "Well, if I'm buying a $40 sweater and they're taking 25% off, then I'm actually paying 75%." Because of course, 75% and 25% add up to 100% which is the full price. So you could also just do one calculation of 0.75 and that's 75% of $40, do that math, and you'll get the 30 in one step. Either way, though, you'll arrive at $30 for the price. 01:53: Now, what about the tax? Well, tax is 6%. So we have to figure out what 6% of our sale price is, $30. So we'll find 6% of 30. Again, translating carefully, 6% becomes 0.06, "of" is still times, and 30 is itself. And multiplying 0.06 times 30, we will get 1.8 which, in money terms, would be $1.80. So $1.80 is the tax. We'd have to add that to the $30 for the item itself, and that would get us a price out the door of $31.80. 02:38: Now, another way you could do that last calculation would be to take the $30 which is your sale price and multiply it by 1.06, 1.06 is kind of made up of two parts. First, there's the one which is 100%, which means just the $30 that you're paying. And of course, 1 times 30 would just be 30. And then there's the 0.06 which is the sales tax. So you're actually paying, if that makes sense, 106% of the price of the $30 because there's an extra 6%. And if you multiply 30 times 1.06, you'll actually get the 31.80 in one step. It's not really required that you do that any more than it's required to do the 75% trick, but it's just kind of nice to see how that works out. It's the same thing as if you get 31.80, the same as if you separately figured out 6%, got the $1.80 and then added the $1.80 to the $30.

Question

Question 1
What is the discount on the sweater?
Responses
A $5$5
B $10$10
C $15$15
Question 2
What is the sale price of the sweater?
Responses
A $30$30
B $40$40
C $50$50
Question 3
What is the sales tax on the sweater?
Responses
A $1.20$1.20
B $1.60$1.60
C $1.80$1.80

Answer 1

Based on the provided information, here are the answers to the questions:

Question 1: What is the discount on the sweater?
Response: B. $10

Question 2: What is the sale price of the sweater?
Response: A. $30

Question 3: What is the sales tax on the sweater?
Response: C. $1.80