Solved on Dec 09, 2023

Find the inn's nightly cost before $6\%$ sales tax, if the total cost per night is $\$ 143.10$ .

STEP 1

Assumptions
1. The total charge per night including sales tax is $143.10.
2. The sales tax rate is 6%.
3. We need to find the cost before tax, which means we need to calculate the original price before the 6% tax was added.

STEP 2

Let's denote the original cost before tax as $C$ . The total cost including tax is the original cost plus the tax on the original cost.
$Total\, cost = C + (Tax\, rate \times C)$

STEP 3

We know the tax rate is 6%, which we need to express as a decimal for calculation purposes.
$6\% = 0.06$

STEP 4

Now, we can rewrite the total cost equation including the decimal form of the tax rate.
$143.10 = C + (0.06 \times C)$

STEP 5

Factor out $C$ from the right side of the equation to simplify the expression.
$143.10 = C(1 + 0.06)$

STEP 6

Now, calculate the factor that includes the tax rate.
$1 + 0.06 = 1.06$

STEP 7

Substitute the calculated factor back into the equation.
$143.10 = C \times 1.06$

STEP 8

To find the original cost $C$ , we need to divide the total cost by the factor that includes the tax rate.
$C = \frac{143.10}{1.06}$

STEP 9

Now, perform the division to find the original cost before tax.
$C = \frac{143.10}{1.06} \approx 135$
The inn's nightly cost before tax is added is approximately $135.

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Find the inn's nightly cost before $6\%$ sales tax, if the total cost per night is $\$ 143.10$ .

STEP 1

Assumptions
1. The total charge per night including sales tax is $143.10.
2. The sales tax rate is 6%.
3. We need to find the cost before tax, which means we need to calculate the original price before the 6% tax was added.

STEP 2

Let's denote the original cost before tax as $C$ . The total cost including tax is the original cost plus the tax on the original cost.
$Total\, cost = C + (Tax\, rate \times C)$

STEP 3

We know the tax rate is 6%, which we need to express as a decimal for calculation purposes.
$6\% = 0.06$

STEP 4

Now, we can rewrite the total cost equation including the decimal form of the tax rate.
$143.10 = C + (0.06 \times C)$

STEP 5

Factor out $C$ from the right side of the equation to simplify the expression.
$143.10 = C(1 + 0.06)$

STEP 6

Now, calculate the factor that includes the tax rate.
$1 + 0.06 = 1.06$

STEP 7

Substitute the calculated factor back into the equation.
$143.10 = C \times 1.06$

STEP 8

To find the original cost $C$ , we need to divide the total cost by the factor that includes the tax rate.
$C = \frac{143.10}{1.06}$

STEP 9

Now, perform the division to find the original cost before tax.
$C = \frac{143.10}{1.06} \approx 135$
The inn's nightly cost before tax is added is approximately $135.

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Find the inn's nightly cost before 6%6\%6% sales tax, if the total cost per night is $143.10\$ 143.10$143.10.

STEP 1

Assumptions1. The total charge per night including sales tax is $143.10.2. The sales tax rate is 6%.3. We need to find the cost before tax, which means we need to calculate the original price before the 6% tax was added.

STEP 2

Let's denote the original cost before tax as CCC. The total cost including tax is the original cost plus the tax on the original cost.Total cost=C+(Tax rate×C)Total\, cost = C + (Tax\, rate \times C)Totalcost=C+(Taxrate×C)

STEP 3

We know the tax rate is 6%, which we need to express as a decimal for calculation purposes.6%=0.066\% = 0.066%=0.06

STEP 4

Now, we can rewrite the total cost equation including the decimal form of the tax rate.143.10=C+(0.06×C)143.10 = C + (0.06 \times C)143.10=C+(0.06×C)

STEP 5

Factor out CCC from the right side of the equation to simplify the expression.143.10=C(1+0.06)143.10 = C(1 + 0.06)143.10=C(1+0.06)

STEP 6

Now, calculate the factor that includes the tax rate.1+0.06=1.061 + 0.06 = 1.061+0.06=1.06

STEP 7

Substitute the calculated factor back into the equation.143.10=C×1.06143.10 = C \times 1.06143.10=C×1.06

STEP 8

To find the original cost CCC, we need to divide the total cost by the factor that includes the tax rate.C=143.101.06C = \frac{143.10}{1.06}C=1.06143.10​

STEP 9

Now, perform the division to find the original cost before tax.C=143.101.06≈135C = \frac{143.10}{1.06} \approx 135C=1.06143.10​≈135The inn's nightly cost before tax is added is approximately $135.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the inn's nightly cost before $6\%$ sales tax, if the total cost per night is $\$ 143.10$ .

Assumptions
1. The total charge per night including sales tax is $143.10.
2. The sales tax rate is 6%.
3. We need to find the cost before tax, which means we need to calculate the original price before the 6% tax was added.

Let's denote the original cost before tax as $C$ . The total cost including tax is the original cost plus the tax on the original cost.
$Total\, cost = C + (Tax\, rate \times C)$

We know the tax rate is 6%, which we need to express as a decimal for calculation purposes.
$6\% = 0.06$

Now, we can rewrite the total cost equation including the decimal form of the tax rate.
$143.10 = C + (0.06 \times C)$

Factor out $C$ from the right side of the equation to simplify the expression.
$143.10 = C(1 + 0.06)$

Now, calculate the factor that includes the tax rate.
$1 + 0.06 = 1.06$

Substitute the calculated factor back into the equation.
$143.10 = C \times 1.06$

To find the original cost $C$ , we need to divide the total cost by the factor that includes the tax rate.
$C = \frac{143.10}{1.06}$

Now, perform the division to find the original cost before tax.
$C = \frac{143.10}{1.06} \approx 135$
The inn's nightly cost before tax is added is approximately $135.