Estimate the original price of each item, and describe your strategy
for each situation
a) You pay $35 for the coat when it is 30% off.
b) You pay $22 for the backpack when it is 15% off.
35 = (1-.3)x =.7x
Solve for x and use the same method for the second problem.
a) To estimate the original price of the coat, we can use the information that it was discounted by 30% and sold for $35.
Step 1: Let's assume the original price of the coat is represented by "x".
Step 2: If the coat is 30% off, we need to find 70% of the original price, which is 0.7x.
Step 3: We know that the coat was sold for $35, so we can set up the equation: 0.7x = $35.
Step 4: To solve for "x", divide both sides of the equation by 0.7: x = $35 / 0.7.
Step 5: Performing the calculation, we find that x = $50.
Therefore, the estimated original price of the coat is $50.
b) Similarly, to estimate the original price of the backpack, we will use the information that it was discounted by 15% and sold for $22.
Step 1: Let's assume the original price of the backpack is represented by "x".
Step 2: If the backpack is 15% off, we need to find 85% of the original price, which is 0.85x.
Step 3: We know that the backpack was sold for $22, so we can set up the equation: 0.85x = $22.
Step 4: To solve for "x", divide both sides of the equation by 0.85: x = $22 / 0.85.
Step 5: Performing the calculation, we find that x ≈ $25.88 (rounded to the nearest cent).
Therefore, the estimated original price of the backpack is approximately $25.88.
In both situations, the strategy was to represent the original price with a variable (x), calculate the percentage of the original price after the discount, set up an equation using the given information, and solve for "x" to find the estimated original price.
To estimate the original price of each item and describe the strategy for each situation, we need to use the concept of percentages and reverse calculations.
a) In situation a, you pay $35 for the coat when it is discounted by 30%. To estimate the original price, we need to calculate what the 30% discount represents in terms of dollars.
1. Convert the percentage discount into a decimal by dividing it by 100: 30% / 100 = 0.30.
2. Multiply the discount decimal by the price you paid to get the discount amount: 0.30 * $35 = $10.50.
3. Subtract the discount amount from the price you paid to find the original price: $35 - $10.50 = $24.50.
The estimated original price of the coat is $24.50.
b) In situation b, you pay $22 for the backpack when it is discounted by 15%. To estimate the original price, we follow a similar process:
1. Convert the percentage discount into a decimal: 15% / 100 = 0.15.
2. Calculate the discount amount by multiplying the discount decimal by the price you paid: 0.15 * $22 = $3.30.
3. Subtract the discount amount from the price you paid to find the original price: $22 - $3.30 = $18.70.
The estimated original price of the backpack is $18.70.
In both situations, the strategy involved converting the percentage discount into a decimal, calculating the discount amount by multiplying the decimal by the price paid, and then subtracting the discount amount from the price paid to find the estimated original price.