Math / Algebra

QuestionFind the marked price and the rate of discount for a camcorder whose price has been reduced by $\$ 70$ and whose sale price is $\$ 287$ .
The marked price is $\$$ $\square$ . (Simplify your answer. Type a whole number or a decimal.) The discount rate is $\square$ \%. (Simplify your answer. Type a whole number or a decimal. Round to the nearest percent if needed.)

Studdy Solution

STEP 1

What is this asking? We need to find the original price of a camcorder and the discount percentage, knowing that the price was reduced by $\$70$ and is now selling for $\$287$ . Watch out! Don't mix up the discount amount with the sale price!
The discount is how much the price was reduced, while the sale price is the final price after the reduction.

STEP 2

1. Find the Original Price
2. Calculate the Discount Rate

STEP 3

Alright, so the camcorder's sale price is $\$287$ , and we know it was reduced by $\$70$ .
To find the original price, we need to add the discount back to the sale price!

STEP 4

Think of it like this: Original Price - Discount = Sale Price.
So, to find the original price, we do Sale Price + Discount = Original Price.

STEP 5

Calculate the Original Price: $\$287 + \$70 = \$357$

STEP 6

So, the original price, also known as the marked price, was $\$\textbf{357}$ !

STEP 7

Now, let's find the discount rate!
The discount rate is the percentage of the original price that was taken off.

STEP 8

To calculate the discount rate, we divide the discount amount by the original price and then multiply by $100$ to express it as a percentage.

STEP 9

Calculate the Discount Rate: $\frac{\text{Discount Amount}}{\text{Original Price}} \cdot 100$ $\frac{\$70}{\$357} \cdot 100$

STEP 10

Now, let's crunch those numbers: $\frac{70}{357} \cdot 100 \approx 0.196 \cdot 100 = 19.6$

STEP 11

The problem asks us to round to the nearest percent, so our discount rate is approximately \textbf{20%}.

STEP 12

The marked price is $\$\textbf{357}$ . The discount rate is \textbf{20%}.

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Studdy Solution

STEP 1

STEP 2

1. Find the Original Price
2. Calculate the Discount Rate

STEP 3

Alright, so the camcorder's sale price is $\$287$ , and we know it was reduced by $\$70$ .
To find the original price, we need to add the discount back to the sale price!

STEP 4

Think of it like this: Original Price - Discount = Sale Price.
So, to find the original price, we do Sale Price + Discount = Original Price.

STEP 5

Calculate the Original Price: $\$287 + \$70 = \$357$

STEP 6

So, the original price, also known as the marked price, was $\$\textbf{357}$ !

STEP 7

Now, let's find the discount rate!
The discount rate is the percentage of the original price that was taken off.

STEP 8

To calculate the discount rate, we divide the discount amount by the original price and then multiply by $100$ to express it as a percentage.

STEP 9

Calculate the Discount Rate: $\frac{\text{Discount Amount}}{\text{Original Price}} \cdot 100$ $\frac{\$70}{\$357} \cdot 100$

STEP 10

Now, let's crunch those numbers: $\frac{70}{357} \cdot 100 \approx 0.196 \cdot 100 = 19.6$

STEP 11

The problem asks us to round to the nearest percent, so our discount rate is approximately \textbf{20%}.

STEP 12

The marked price is $\$\textbf{357}$ . The discount rate is \textbf{20%}.

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Studdy Solution

STEP 1

STEP 2

1. Find the Original Price2. Calculate the Discount Rate

STEP 3

Alright, so the camcorder's sale price is $287\$287$287, and we know it was reduced by $70\$70$70.To find the original price, we need to add the discount back to the sale price!

STEP 4

Think of it like this: Original Price - Discount = Sale Price.So, to find the original price, we do Sale Price + Discount = Original Price.

STEP 5

**Calculate the Original Price:** $287+$70=$357 \$287 + \$70 = \$357 $287+$70=$357

STEP 6

So, the **original price**, also known as the **marked price**, was $357\$\textbf{357}$357!

STEP 7

Now, let's find the discount rate!The discount rate is the percentage of the original price that was taken off.

STEP 8

To calculate the discount rate, we divide the **discount amount** by the **original price** and then multiply by 100100100 to express it as a percentage.

STEP 9

**Calculate the Discount Rate:** Discount AmountOriginal Price⋅100 \frac{\text{Discount Amount}}{\text{Original Price}} \cdot 100 Original PriceDiscount Amount​⋅100 $70$357⋅100 \frac{\$70}{\$357} \cdot 100 $357$70​⋅100

STEP 10

Now, let's crunch those numbers: 70357⋅100≈0.196⋅100=19.6 \frac{70}{357} \cdot 100 \approx 0.196 \cdot 100 = 19.6 35770​⋅100≈0.196⋅100=19.6

STEP 11

The problem asks us to round to the nearest percent, so our **discount rate** is approximately \textbf{20%}.

STEP 12

The marked price is $357\$\textbf{357}$357. The discount rate is \textbf{20%}.

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1. Find the Original Price
2. Calculate the Discount Rate

Alright, so the camcorder's sale price is $\$287$ , and we know it was reduced by $\$70$ .
To find the original price, we need to add the discount back to the sale price!

Think of it like this: Original Price - Discount = Sale Price.
So, to find the original price, we do Sale Price + Discount = Original Price.

Calculate the Original Price: $\$287 + \$70 = \$357$

So, the original price, also known as the marked price, was $\$\textbf{357}$ !

Now, let's find the discount rate!
The discount rate is the percentage of the original price that was taken off.

To calculate the discount rate, we divide the discount amount by the original price and then multiply by $100$ to express it as a percentage.

Calculate the Discount Rate: $\frac{\text{Discount Amount}}{\text{Original Price}} \cdot 100$ $\frac{\$70}{\$357} \cdot 100$

Now, let's crunch those numbers: $\frac{70}{357} \cdot 100 \approx 0.196 \cdot 100 = 19.6$

The problem asks us to round to the nearest percent, so our discount rate is approximately \textbf{20%}.

The marked price is $\$\textbf{357}$ . The discount rate is \textbf{20%}.