Math / Algebra

QuestionA local Barnes and Noble paid a $\$ 80.35$ net price for each hardbound atlas. The publisher offered a $15 \%$ trade discount. What was the publisher's list price?
Note: Round your answer to the nearest cent.

Studdy Solution

STEP 1

1. The net price is given as $\$80.35$ .
2. A trade discount of $15\%$ was applied to the list price to arrive at the net price.
3. The list price is the price before the trade discount was applied.
4. The final answer should be rounded to the nearest cent.

STEP 2

1. Define the relationship between the list price, trade discount, and net price.
2. Set up the equation to solve for the list price.
3. Solve the equation for the list price.
4. Round the list price to the nearest cent.

STEP 3

Define the relationship between the list price (denoted as $P$ ), the trade discount (denoted as $d$ ), and the net price (denoted as $N$ ).
The net price is given by: $N = P \times (1 - d)$
Given: $N = 80.35$ $d = 0.15$

STEP 4

Set up the equation based on the relationship defined in STEP_1. Substitute the known values into the equation:
$80.35 = P \times (1 - 0.15)$

STEP 5

Simplify the equation to solve for $P$ :
$80.35 = P \times 0.85$
To isolate $P$ , divide both sides by $0.85$ :
$P = \frac{80.35}{0.85}$

STEP 6

Calculate the value of $P$ :
$P = \frac{80.35}{0.85} \approx 94.53$

STEP 7

Round the list price to the nearest cent. In this case, the calculated value is already to the nearest cent, so:
$P = 94.53$
The publisher's list price was $\$94.53$ .

Was this helpful?

QuestionA local Barnes and Noble paid a $\$ 80.35$ net price for each hardbound atlas. The publisher offered a $15 \%$ trade discount. What was the publisher's list price?
Note: Round your answer to the nearest cent.

Studdy Solution

STEP 1

1. The net price is given as $\$80.35$ .
2. A trade discount of $15\%$ was applied to the list price to arrive at the net price.
3. The list price is the price before the trade discount was applied.
4. The final answer should be rounded to the nearest cent.

STEP 2

1. Define the relationship between the list price, trade discount, and net price.
2. Set up the equation to solve for the list price.
3. Solve the equation for the list price.
4. Round the list price to the nearest cent.

STEP 3

Define the relationship between the list price (denoted as $P$ ), the trade discount (denoted as $d$ ), and the net price (denoted as $N$ ).
The net price is given by: $N = P \times (1 - d)$
Given: $N = 80.35$ $d = 0.15$

STEP 4

Set up the equation based on the relationship defined in STEP_1. Substitute the known values into the equation:
$80.35 = P \times (1 - 0.15)$

STEP 5

Simplify the equation to solve for $P$ :
$80.35 = P \times 0.85$
To isolate $P$ , divide both sides by $0.85$ :
$P = \frac{80.35}{0.85}$

STEP 6

Calculate the value of $P$ :
$P = \frac{80.35}{0.85} \approx 94.53$

STEP 7

Round the list price to the nearest cent. In this case, the calculated value is already to the nearest cent, so:
$P = 94.53$
The publisher's list price was $\$94.53$ .

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionA local Barnes and Noble paid a $80.35\$ 80.35$80.35 net price for each hardbound atlas. The publisher offered a 15%15 \%15% trade discount. What was the publisher's list price?Note: Round your answer to the nearest cent.

Studdy Solution

STEP 1

1. The net price is given as $80.35 \$80.35$80.35.2. A trade discount of 15%15\%15% was applied to the list price to arrive at the net price.3. The list price is the price before the trade discount was applied.4. The final answer should be rounded to the nearest cent.

STEP 2

1. Define the relationship between the list price, trade discount, and net price.2. Set up the equation to solve for the list price.3. Solve the equation for the list price.4. Round the list price to the nearest cent.

STEP 3

Define the relationship between the list price (denoted as PPP), the trade discount (denoted as ddd), and the net price (denoted as NNN). The net price is given by: N=P×(1−d) N = P \times (1 - d) N=P×(1−d)Given: N=80.35 N = 80.35 N=80.35 d=0.15 d = 0.15 d=0.15

STEP 4

Set up the equation based on the relationship defined in STEP_1. Substitute the known values into the equation:80.35=P×(1−0.15) 80.35 = P \times (1 - 0.15) 80.35=P×(1−0.15)

STEP 5

Simplify the equation to solve for PPP:80.35=P×0.85 80.35 = P \times 0.85 80.35=P×0.85To isolate PPP, divide both sides by 0.850.850.85:P=80.350.85 P = \frac{80.35}{0.85} P=0.8580.35​

STEP 6

Calculate the value of PPP:P=80.350.85≈94.53 P = \frac{80.35}{0.85} \approx 94.53 P=0.8580.35​≈94.53

STEP 7

Round the list price to the nearest cent. In this case, the calculated value is already to the nearest cent, so:P=94.53 P = 94.53 P=94.53 The publisher's list price was $94.53\$94.53$94.53.

Get Studdy

Studdy solves anything!

Start learning now

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

QuestionA local Barnes and Noble paid a $\$ 80.35$ net price for each hardbound atlas. The publisher offered a $15 \%$ trade discount. What was the publisher's list price?
Note: Round your answer to the nearest cent.

1. The net price is given as $\$80.35$ .
2. A trade discount of $15\%$ was applied to the list price to arrive at the net price.
3. The list price is the price before the trade discount was applied.
4. The final answer should be rounded to the nearest cent.

1. Define the relationship between the list price, trade discount, and net price.
2. Set up the equation to solve for the list price.
3. Solve the equation for the list price.
4. Round the list price to the nearest cent.

Define the relationship between the list price (denoted as $P$ ), the trade discount (denoted as $d$ ), and the net price (denoted as $N$ ).
The net price is given by: $N = P \times (1 - d)$
Given: $N = 80.35$ $d = 0.15$

Set up the equation based on the relationship defined in STEP_1. Substitute the known values into the equation:
$80.35 = P \times (1 - 0.15)$

Simplify the equation to solve for $P$ :
$80.35 = P \times 0.85$
To isolate $P$ , divide both sides by $0.85$ :
$P = \frac{80.35}{0.85}$

Calculate the value of $P$ :
$P = \frac{80.35}{0.85} \approx 94.53$

Round the list price to the nearest cent. In this case, the calculated value is already to the nearest cent, so:
$P = 94.53$
The publisher's list price was $\$94.53$ .