MATH SOLVE

3 months ago

Q:
# Chris and Kate’s dinner bill, including a 20% tip, is $95.40. What was the amount of the bill before the tip?

Accepted Solution

A:

Answer:It is $79.50Step-by-step explanation:the base annotation indicator is the number of which we are taking a percentage and the amounttext annotation indicator is the value that results from taking the percent of the base. This means that in any percent problem, there are three basic values to be concerned about: the percent, the base, and the resulting amount. A percentage problem may ask us to find any one of these three values.
The Basic Percent Equationtext annotation indicator is the basic relationship that we need to learn to understand. We need to know how to identify which number is the base and which number is the amount?
Example: Suppose you go out to dinner at a restaurant. After dinner when you pay your bill, you decide to give your server a 15% tip. If the total bill (before tipping) is $20.00, then how much should you leave as a tip?
We can restate the problem as: 15% of the total bill of $20 is the tip.
The base in this case is the total bill of $20.00, since this is the value we are taking a percentage of. We solve for the tip which is the resulting amount.
(percent) × (base) = (amount)
(percent) × (bill) = (tip)
(15%) × ($20) = x
where x represents the amount of the tip.
Next, we convert the percent to either fraction or decimal form and then multiply:
x = (0.15)(20)
x = 3
You would tip the server $3.
Example: You live in a city that charges 6% sales tax on all purchases. If you go to a store and purchase $30 worth of merchandise, what is your total bill?
We can restate the sales tax portion of the problem as: 6% of the $30 worth of merchandise is the sales tax.
Next, we compute the tax on the purchase using the Basic Percent Equationtext annotation indicator. We do not know the amount of sales tax, so we let x represent the amount of sales tax in the equation and solve for x.
(percent) × (base) = (amount)
(6%) × ($30) = (amount of tax)
We compute
(0.06)(30) = x
1.80 = x
The amount of tax is $1.80. Notice that this does not give the total bill. It only gives the amount of tax paid on the purchase. To compute the total bill, we add the amount of tax on to the cost of the merchandise.
Since $30.00 + $1.80 = $31.80, the total bill is $31.80.
We may also solve the problem in a single equation.
Second Method for the above problem: You live in a city that charges 6% sales tax on all purchases. If you go to a store and purchase $30 worth of merchandise, what is your total bill?
Note that you will pay 100% of the cost plus 6% for sales tax, so you will pay 106% of the cost of the merchandise.
We restate the problem as: 106% of the $30 worth of merchandise is the total cost.
Next, we compute the tax on the purchase using the Basic Percent Equationtext annotation indicator. We do not know the total cost, so we let x represent the amount of the total cost in the equation and solve for x.
(percent) × (base) = (amount)
(106%) × ($30) = (amount of the total cost)
We compute
(1.06)(30) = x
31.80 = x
The total bill is $31.80.
For the next examples, formulate each part for yourself before checking.I really hop ethis helped. God bless you and have a great day! :-)