The regular price of a sleeping bag is
$39.95. It is on sale for 20% off.
There is a 13% sales tax. The discount
is usually applied before the tax is
added. Suppose the tax is calculated
first. Would the total cost be more or
less in this case? Explain.
please I'm desperate. I'm barely passing math with my grades and this will be a lot of help
discount first: 29.95 * 0.80 * 1.13
tax first: 29.95 * 1,13 * 0.80
since multiplication is commutative, it gives the same answer.
by using the discount first, the amount taxed is less
by taxing first, the discount is more
If the tax is calculated first, the total cost would be more compared to applying the discount first.
Let's calculate the total cost using this order:
1. Calculate the tax first:
13% of the regular price ($39.95) = $5.19
2. Apply the discount:
20% off the regular price = $39.95 * 0.20 = $7.99
3. Subtract the discount from the original price:
$39.95 - $7.99 = $31.96
4. Add the tax:
$31.96 + $5.19 = $37.15
So, if the tax is calculated first, the total cost is $37.15, which is more than if the discount is applied first.
To determine whether the total cost would be more or less if the tax is calculated before the discount, we can calculate the total cost in both scenarios.
First, let's calculate the total cost when the discount is applied before the tax:
1. Calculate the discounted price:
The sleeping bag is on sale for a 20% discount. To find the discount, multiply the regular price ($39.95) by the discount percentage:
Discount = $39.95 x 0.20 = $7.99
Subtract the discount from the regular price to find the discounted price:
Discounted Price = $39.95 - $7.99 = $31.96
2. Calculate the total cost including tax:
To find the tax, multiply the discounted price by the tax rate of 13%:
Tax = $31.96 x 0.13 = $4.15
Add the tax to the discounted price to find the total cost:
Total Cost = $31.96 + $4.15 = $36.11
Therefore, if the discount is applied before the tax, the total cost would be $36.11.
Now, let's calculate the total cost if the tax is calculated first:
1. Calculate the tax amount:
To find the tax, multiply the regular price ($39.95) by the tax rate of 13%:
Tax = $39.95 x 0.13 = $5.19
2. Calculate the discounted price after tax:
Subtract the tax amount from the regular price to find the amount before the discount:
Amount Before Discount = $39.95 - $5.19 = $34.76
To find the discounted price, apply the 20% discount to the amount before the discount:
Discounted Price = $34.76 x 0.20 = $6.95
3. Calculate the total cost:
Add the discounted price to the tax amount to find the total cost:
Total Cost = $34.76 + $6.95 = $41.71
Therefore, if the tax is calculated first, the total cost would be $41.71.
Comparing the two scenarios, we can see that if the tax is calculated first, the total cost is higher ($41.71) compared to when the discount is applied first ($36.11). Therefore, the total cost would be more if the tax is calculated first rather than if the discount is applied before the tax.