Math / Numbers & Operations

Question1W 1:00-2:15pm (Section 096) - iCollege Jaiden Sargent 09/08/24 Models and Applications Question 8, 1.3-12 HW Score: $63.64 \%, 7$ of 11 points Points: 0 of 1 Inclusive of a $7.7 \%$ sales tax, a diamond ring sold for $\$ 2,046.30$ . Find the price of the ring before the tax was added. (Round to the nearest cent, if necessary.) A. $\$ 157.57$ B. $\$ 1,888.73$ C. $\$ 1,900.00$ D. $\$ 2,203.87$

Studdy Solution

STEP 1

1. The total price of the diamond ring after including the sales tax is $\$2,046.30$ .
2. The sales tax rate is $7.7\%$ .
3. We need to find the original price of the ring before the tax was added.
4. The price before tax should be rounded to the nearest cent.

STEP 2

1. Express the relationship between the total price, the original price, and the sales tax.
2. Set up the equation to solve for the original price before tax.
3. Solve the equation for the original price.
4. Round the solution to the nearest cent, if necessary.
5. Verify the solution by checking the options given.

STEP 3

Express the relationship between the total price ( $P_{\text{total}}$ ), the original price ( $P_{\text{original}}$ ), and the sales tax rate ( $r$ ).
$P_{\text{total}} = P_{\text{original}} \times (1 + r)$
Given: $P_{\text{total}} = 2046.30$ $r = 0.077$

STEP 4

Set up the equation to solve for $P_{\text{original}}$ .
$2046.30 = P_{\text{original}} \times (1 + 0.077)$

STEP 5

Simplify the equation to isolate $P_{\text{original}}$ .
$2046.30 = P_{\text{original}} \times 1.077$ $P_{\text{original}} = \frac{2046.30}{1.077}$

STEP 6

Calculate $P_{\text{original}}$ .
$P_{\text{original}} = \frac{2046.30}{1.077} \approx 1899.999$

STEP 7

Round the price to the nearest cent.
$P_{\text{original}} \approx 1900.00$

STEP 8

Verify the solution with the given options:
The computed value $1900.00$ matches option C.
The price of the ring before the tax was added is $\$ 1900.00$ .

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Studdy Solution

STEP 1

1. The total price of the diamond ring after including the sales tax is $\$2,046.30$ .
2. The sales tax rate is $7.7\%$ .
3. We need to find the original price of the ring before the tax was added.
4. The price before tax should be rounded to the nearest cent.

STEP 2

STEP 3

Express the relationship between the total price ( $P_{\text{total}}$ ), the original price ( $P_{\text{original}}$ ), and the sales tax rate ( $r$ ).
$P_{\text{total}} = P_{\text{original}} \times (1 + r)$
Given: $P_{\text{total}} = 2046.30$ $r = 0.077$

STEP 4

Set up the equation to solve for $P_{\text{original}}$ .
$2046.30 = P_{\text{original}} \times (1 + 0.077)$

STEP 5

Simplify the equation to isolate $P_{\text{original}}$ .
$2046.30 = P_{\text{original}} \times 1.077$ $P_{\text{original}} = \frac{2046.30}{1.077}$

STEP 6

Calculate $P_{\text{original}}$ .
$P_{\text{original}} = \frac{2046.30}{1.077} \approx 1899.999$

STEP 7

Round the price to the nearest cent.
$P_{\text{original}} \approx 1900.00$

STEP 8

Verify the solution with the given options:
The computed value $1900.00$ matches option C.
The price of the ring before the tax was added is $\$ 1900.00$ .

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Studdy Solution

STEP 1

1. The total price of the diamond ring after including the sales tax is $2,046.30\$2,046.30$2,046.30.2. The sales tax rate is 7.7%7.7\%7.7%.3. We need to find the original price of the ring before the tax was added.4. The price before tax should be rounded to the nearest cent.

STEP 2

STEP 3

STEP 4

Set up the equation to solve for PoriginalP_{\text{original}}Poriginal​.2046.30=Poriginal×(1+0.077) 2046.30 = P_{\text{original}} \times (1 + 0.077) 2046.30=Poriginal​×(1+0.077)

STEP 5

Simplify the equation to isolate PoriginalP_{\text{original}}Poriginal​.2046.30=Poriginal×1.077 2046.30 = P_{\text{original}} \times 1.077 2046.30=Poriginal​×1.077 Poriginal=2046.301.077 P_{\text{original}} = \frac{2046.30}{1.077} Poriginal​=1.0772046.30​

STEP 6

Calculate PoriginalP_{\text{original}}Poriginal​.Poriginal=2046.301.077≈1899.999 P_{\text{original}} = \frac{2046.30}{1.077} \approx 1899.999 Poriginal​=1.0772046.30​≈1899.999

STEP 7

Round the price to the nearest cent.Poriginal≈1900.00 P_{\text{original}} \approx 1900.00 Poriginal​≈1900.00

STEP 8

Verify the solution with the given options:The computed value 1900.001900.001900.00 matches option C. The price of the ring before the tax was added is $1900.00\$ 1900.00$1900.00.

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1. The total price of the diamond ring after including the sales tax is $\$2,046.30$ .
2. The sales tax rate is $7.7\%$ .
3. We need to find the original price of the ring before the tax was added.
4. The price before tax should be rounded to the nearest cent.

Set up the equation to solve for $P_{\text{original}}$ .
$2046.30 = P_{\text{original}} \times (1 + 0.077)$

Simplify the equation to isolate $P_{\text{original}}$ .
$2046.30 = P_{\text{original}} \times 1.077$ $P_{\text{original}} = \frac{2046.30}{1.077}$

Calculate $P_{\text{original}}$ .
$P_{\text{original}} = \frac{2046.30}{1.077} \approx 1899.999$

Round the price to the nearest cent.
$P_{\text{original}} \approx 1900.00$

Verify the solution with the given options:
The computed value $1900.00$ matches option C.
The price of the ring before the tax was added is $\$ 1900.00$ .