Question

1. shirts are on sale for 20% off. you buy two of them. as you pay, the cashier says, “20% off of each shirt means 40% off of the total price. do you agree or disagree? explain why.

Explanation:

Step1: Define Variables

Let the original price of one shirt be $p$. Then the original total price for two shirts is $2p$.

Step2: Calculate 20% Off Each Shirt

For one shirt, the discount is $20\%$ of $p$, so the discounted price of one shirt is $p - 0.2p = 0.8p$. For two shirts, the total discounted price is $2\times0.8p = 1.6p$.

Step3: Calculate 40% Off Total Price

The total original price is $2p$. A $40\%$ discount on the total price would give a discounted price of $2p - 0.4\times2p = 2p - 0.8p = 1.2p$.

Step4: Compare the Two Discounts

We see that $1.6p
eq1.2p$. So a 20% discount on each shirt (total discount of 20% of the sum of two shirts' original prices, since $2\times0.2p = 0.4p$ and $0.4p$ is 20% of $2p$) is not the same as a 40% discount on the total price.

Answer:

I disagree. Let the original price of one shirt be $p$. Total original price for two shirts: $2p$.

• 20% off each shirt: Discount per shirt = $0.2p$, total discount = $2\times0.2p = 0.4p$ (20% of $2p$), total price = $2p - 0.4p = 1.6p$.
• 40% off total price: Discount = $0.4\times2p = 0.8p$, total price = $2p - 0.8p = 1.2p$.

Since $1.6p
eq1.2p$, the two discounts are not equivalent.