if the Cost of meal = $8.50 Discount offered = 15% Sales tax = 5% then what would the Actual price = $

Answer 1

In this case, we need to understand what it means mathematically to receive a discount or to add a surcharge (like sales tax). When we add 5% of something, we are taking the original (say, a variable 'x'), and adding 5% of that vaiable's value to the total, so we would get something like this for the equation of just the sales tax:

y = x + 0.05x.

Now, if we use the distributive property of multiplication to factor the x out of the right side of the equation, we get y = x * (1 + 0.05) = x * 1.05. This means that a 5% sales tax is equivalent to multiplying the original number by 1.05.

Next, let's consider the discount. Similar to the tax, we are subtracting a percentage of the original variable from itself in order to get the answer, so we can put it into equation form like this:

y = x - 0.15x; but, by the same method by which we factored out the x in the sales tax problem, we can factor out the x in this problem as well:

y = x * (1 - 0.15) = x * 0.85.

So, we can see that, if we want to apply both a discount and a sales tax, we would just do the following:

y = x * 0.85 * 1.05

Now, you might be wondering "Does it matter whether I put the sales tax or the discount first?" Thankfully, it doesn't matter, because of the commutative property of multiplication. Thus, x * 0.85 * 1.05 = x * 1.05 * 0.85

Finally, we complete the multiplication, substituting 8.50 for x: x * 0.85 * 1.05 = 7.59

Answer 2

TC= total cost of the items

TC= $8.50

-15% discount+sale tax of 5%=AP. AP actual price.

15/100 = 0.15. and 5/100= 0.05

0.15x +0.05x =8.50

0.20 x=8.50

x= 8.50/0.20 = $42.50

Your actual price = $42.50.

This how you check your answer.

15% of 42.50 = $ 6.375

5% of $42.50 = $2.125

$6.375 + $2.125 =. $8.50. ...............which is the total cost of the meal.