Answer :
To determine the original price of the item that Joyce paid $152.00 for at a 20% discount, follow these steps:
1. Understand the given values:
- Payment made: $152.00
- Discount: 20%
2. Express the discount percentage as a decimal:
- A 20% discount is equivalent to a 20/100 fraction or a 0.20 decimal.
3. Determine the sale price equation:
- Let's denote the original price as \( P \).
- Since Joyce received a 20% discount, she paid 80% of the original price.
- Therefore, the relationship between the payment and the original price is given by:
[tex]\[ \text{Payment} = \text{Original Price} \times (1 - \text{Discount}) \][/tex]
Substituting the given values:
[tex]\[ 152.00 = P \times (1 - 0.20) \][/tex]
4. Simplify the equation:
- Subtract the discount from 1:
[tex]\[ 152.00 = P \times 0.80 \][/tex]
5. Solve for the original price \( P \):
- Divide both sides of the equation by 0.80:
[tex]\[ P = \frac{152.00}{0.80} \][/tex]
6. Calculate the division:
- Perform the calculation to find \( P \):
[tex]\[ P = 190.00 \][/tex]
7. Round to the nearest cent (if needed):
- In this case, the calculation comes out exactly to $190.00, so there is no need for further rounding.
Therefore, the original price of the item was $190.00.
1. Understand the given values:
- Payment made: $152.00
- Discount: 20%
2. Express the discount percentage as a decimal:
- A 20% discount is equivalent to a 20/100 fraction or a 0.20 decimal.
3. Determine the sale price equation:
- Let's denote the original price as \( P \).
- Since Joyce received a 20% discount, she paid 80% of the original price.
- Therefore, the relationship between the payment and the original price is given by:
[tex]\[ \text{Payment} = \text{Original Price} \times (1 - \text{Discount}) \][/tex]
Substituting the given values:
[tex]\[ 152.00 = P \times (1 - 0.20) \][/tex]
4. Simplify the equation:
- Subtract the discount from 1:
[tex]\[ 152.00 = P \times 0.80 \][/tex]
5. Solve for the original price \( P \):
- Divide both sides of the equation by 0.80:
[tex]\[ P = \frac{152.00}{0.80} \][/tex]
6. Calculate the division:
- Perform the calculation to find \( P \):
[tex]\[ P = 190.00 \][/tex]
7. Round to the nearest cent (if needed):
- In this case, the calculation comes out exactly to $190.00, so there is no need for further rounding.
Therefore, the original price of the item was $190.00.
Step-by-step explanation:
whenever you have a question about %, you need to find 100% or 1% (whatever comes easier) abs the calculate the rest of if this.
$152.00 was already 20% off the original price.
the original price was therefore 100%.
and $152 is 100%-20% = 80%
1% = 80%/80 = 152/80 = $1.90
100% = 1%×100 = 1.90 × 100 = $190.00
so, the original price for the item was $190.00
