We would like to eliminate .

Hence we multiply the first equation by which gives us the following equations:

Adding the above two equations eliminates the variable . We are left with:

and so

Replacing with in the original equation gives us

solving for gives us

Hence the solution is .

Determine how much Billy has spent on all twenty gold coins. Since he bought 20 gold coins at wholesale price, multiply 20 by the price of gold at \$100.

Billy has spent on gold coins at wholesale price.

Determine his profit after he sells all gold coins at each.

This amount is his revenue after selling all his 20 coins.

Profit is the total revenue minus the cost Billy has spent.

After subtracting the initial cost, Billy has \$600 profit from selling all his 20 gold coins at \$130 each.

Divide the profit with the retail cost of the gold coins to determine how many gold coins he can buy at retail price with his profit.

Billy can only buy gold coins at retail price as a result of his profit.

The answer is:

Billy's profit comes from the earnings of all stocks minus the amount that he initially invested.

Find out how much Billy has spent on the fifteen stocks. Multiply the cost of the stock by the amount he has bought.

He spent seventy five dollars on the stocks.

Find out the total amount he has sold all the stocks for. Multiply the new price of the stocks by the amount he has sold.

Billy's profit is the difference of the earnings minus the initial price of all the stocks. Subtract the two prices.

Billy's profit is .

Take the root.

Subtract from both sides.

Divide both sides by and simplify.

Let be the percent. Then

County A: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!

$75 * 0.0725 = $5.4375

Add the original price and the sales tax.

$75 + $5.4375 = \$80.4375

County B: Multiply the price by the sales tax to find out how much money the sales tax will add. Remember to convert percent to decimal!

\$70 * 0.08 = \$5.6

Add the original price and the sales tax.

\$70 + $5.6 = $75.6

Then take the difference.

80.4375 – 75.6 = 4.8375

Round to the nearest hundredth: \$4.84

How to calculate the amount of sales tax?

1. Convert tax percentage into a decimal by moving the decimal point two spaces to the left.
2. Multiple the pre-tax value by the newly calculated decimal value in order to find the cost of the sales tax.
3. Add the sales tax value to the pre-tax value to calculate the total cost.

Calculating sales tax at time of purchase:

In order to calculate the sales tax of an item, we need to first multiply the pre-tax cost of the item by the sales tax percentage after it has been converted into a decimal. Once the sales tax has been calculated it needs to be added to the pre-tax value in order to find the total cost of the item. Let's start by working with an example. If a magazine costs \$2.35 and has a 6% sales tax, then what is the total cost of the item. First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

Calculating the sales tax percentage of a total:

If we are given the total cost of an item or group of items and the pre-tax cost of the good(s), then we can calculate the sales tax percentage of the total cost. First, we need to subtract the pre-tax value from the total cost of the purchase. Next, we need to create a ratio of the sales tax to the pre-tax cost off the items. Last, we need to create a proportion where the pre-tax cost is related to 100% and solve for the percentage of the sales tax. Let's start by working through an example. If a person pays \$245.64 for groceries that cost \$220.00 pre tax, then what is the sales tax percentage for the items.

First, subtract the pre-tax value from the total cost of the items to find the sales tax cost.

Next, create a ratio of the sales tax to the pre-tax cost of the items.

Last, create a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

Cross multiply and solve.

Isolate the sales tax percentage to the left side of the equation by dividing each side by the pre-tax value.

Round to two decimal places since our answer is in dollars and cents.

Last, we can check this answer by calculating the sales tax percentage of the total as seen previously.

First, we need to convert the sales tax percentage into a decimal by moving the point two spaces to the left.

Now, we need to multiply the pre-tax cost of this item by this value in order to calculate the sales tax cost.

Round to two decimal places since our total is in dollars and cents.

Last, add this value to the pre-tax value of the item to find the total cost.

Our answers check out; therefore they are correct. Now, let's use this information to solve the given problem.

Solution:

If Robb buys a new horse for \$4,566 in a county with a sales tax of 5%, how much does he pay in tax?

To solve this question, begin by changing our percent into a decimal. To do so, we move the decimal point two places to the left.

Next, simply multiple the price of the horse by the sales tax:

So Robb pays an additional \$228.30

Since percentages are out of 100%, start first by dividing the percentage by 100 to convert it to a fraction.

Simplify the fraction to lowest terms by dividing the numerator (top) and denominator (bottom) by the same number or greatest common factor you can think of. In this case, since both 66 and 100 are even numbers, I know that 2 is a factor so I will divide both numbers by 2.

I check again if anything divides into both the top and the bottom but nothing does so this must be the fraction reduced to lowest terms.

In order to change a percent into a fraction, the first step is to take the percent and place it over 100:

Then simplify as needed:

For this question the final answer will be 21/50

To find the fractional equivalent of a percent, we place that number over 100 and reduce the fraction: