Answer:
1. 1.00 for the prices, 0.06 for the taxes
2. B. t= 0.06p
3. A. $0.94
5. 1.00 + 0.06 = 1.06, 2.00 + 0.12 = 2.12, 3.00 + 0.18 = 3.18, 4.00 + 0.24 = 4.24
6. B: 1.06
7. D. T=1.06s
Step-by-step explanation:
1. Price: 1.00| 2.00| 3.00| 4.00| Sales Tax: 0.06, 012, 0.18, 024,
Find the constant of variation, k, for the above table. What does this represent?
The constant of variation is the fixed amount that is added or subtracted from one element of a data series to find the next one. So, since you have 2 different data sets (one for price, one for taxes), we in fact have two series, 2 constants of variation.
For the price... it goes from 1.00 to 2.00 to 3.00 to 4.00. We can see it increases by 1.00 each single time, that is the constant of variation for the prices!
If we look at the taxes, we see a similar progression... from 0.06 to 0.12 to 0.18 to 0.24... it changes by 0.06 each time. 0.06 is then the constant of variation for the taxes part of the table.
2. What is the direct variation equation for the table above, using t for sales tax and p for price?
B. t= 0.06p
If you look at the relationship between the elements of the price table and the corresponding elements of the tax table, you'll see a clear ratio of 6% (0.06/1.00, 0.12/2.00, 0.18/3.00 and so on).
So, to obtain the tax number (t), you need to multiply the price of the sale (p) by 0.06. And you can easily verify it by using the 2.00 sale for example:
t = 0.06 * 2.00 = 0.12
3. What is the sales tax on a purchase of $15.60
A. $0.94
It's easy to calculate with the formula we just found in the previous question: t= 0.06p
So, if we use it with the price of $15.60, we get:
t = 0.06 * $15.60 = $0.936
Since we don't use half cents anymore, we have to round it to the closest cent. In that case, we would round it up to $0.94.
5. Price: 1.00, 2.00, 3.00, 4.00, From the closing question what are the entries for the column total price plus sales tax in the above table?
To calculate the total price for each sale, we need to add up the price of the item plus the amount of tax for that sale. We already have both amounts, so it's easy:
1.00 + 0.06 = 1.06
2.00 + 0.12 = 2.12
3.00 + 0.18 = 3.18
4.00 + 0.24 = 4.24
6. What is the value of the constant of variation, k, for the above table?
Again, the constant of variation is the fixed amount that is added or subtracted from one element of a data series to find the next one. The answer choices (0.06, 1.06, 2.12, 4.24) lead to think they're talking about the total price amounts (since 3 of the 4 possible answers are total amounts we just calculated), so we'll use this sample.
The amounts go from 1.06 to 2.12 to 3.18 to 4.24, if you subtract any element of the series from the next element, you'll get 1.06, that's the constant of progression. In this case, 1.06.
7. Which is the direct variation equation for the table in question 5 using "s" for sale price and "T" for total price?
So, if we look at the data, we have the following relationship:
sale 1.00, total 1.06
sale 2.00, total 2.12
sale 3.00, total 3.18
sale 4.00, total 4.24
What relation can we establish based on that? What's the relation between the total price and the sale price? Take any set, and divide the total by the sale...
Let's take 3.18 / 3.00 = 1.06, and it works the same for all other total/sale.
So, the relation is 1.06. You have to multiply the sale amount by 1.06 to get the total amount (which includes tax).
so, T = 1.06s
