Roberto is an employee of a store and receives 20% discount off all items in the store. During a sale, the price of a jacket is reduced by $15. Roberto will receive both his 20% discount and the $15 off. Which is better for Roberto, to take the 20% discount first and then subtract $15 or to subtract $15 first and then take his 20% discount? Explain you answer.
To determine which option is better for Roberto, let's go through both scenarios step-by-step:
Option 1: Taking the 20% discount first and then subtracting $15:
1. Let's assume the original price of the jacket is "P."
2. Roberto's 20% discount will be calculated as 20% of "P", which is 0.20 * P.
3. After applying the discount, the new price will be "P - 0.20 * P" or 0.80 * P.
4. Now, Roberto subtracts the $15 discount from the new price, which will be 0.80 * P - $15.
Option 2: Subtracting $15 first and then taking the 20% discount:
1. Roberto starts by subtracting the $15 discount from the original price, which will be "P - $15".
2. After subtracting the $15, the new price will be "P - $15."
3. Now, Roberto applies his 20% discount to the new price, which will be 0.20 * (P - $15).
To find out which option is better, we need to compare the two final expressions (0.80 * P - $15 in Option 1 vs. 0.20 * (P - $15) in Option 2) and see which value is greater.
It is not possible to determine which option is better without knowing the value of "P". Depending on the original price of the jacket, one option may provide greater savings compared to the other option. Thus, without further information, it is difficult to determine which option is more beneficial for Roberto.
To determine which option is better for Roberto, we can compare both scenarios and calculate the final price under each approach.
Option 1: Taking the 20% discount first and then subtracting $15
Let's assume the original price of the jacket is P.
Step 1: Calculate the price after the 20% discount
The price after the 20% discount would be (P - 20% of P) = (P - 0.2P) = 0.8P.
Step 2: Subtract $15 from the discounted price
The final price after subtracting $15 would be (0.8P - 15).
Option 2: Subtracting $15 first and then taking the 20% discount
Let's follow a similar approach.
Step 1: Subtract $15 from the original price
The price after subtracting $15 would be (P - $15).
Step 2: Calculate the price after the 20% discount on the reduced price
The discounted price after the 20% discount would be ((P - $15) - 20% of (P - $15)) = ((P - $15) - 0.2(P - $15)).
Now, to determine which option is better, we need to compare the two final prices obtained from each scenario. If the final price in Option 1 is lower than the final price in Option 2, then Option 1 is better for Roberto. Conversely, if the final price in Option 2 is lower, then Option 2 is better.
By comparing the two scenarios, we can find out which option yields the better benefit for Roberto.