Shop A sold a notebook for $1200. This was 125% of the price of a similar notebook sold in Shop B. Find the price of the notebook in Shop B.
During a sale, both shops gave the same percentage of discount. Dennis bought the notebook from Shop B and found that she paid $175.20 less than the discounted price in Shop A.
What is the percentage discount given during the sale?
1. 1.25P = 1200.
P = 1200 / 1.25 = $960
2. 960-960r = 1200-1200r - 175.20.
960-960r = -1200r + 1024.80.
-960r + 1200r = 1024.80 - 960.
240r = 64.8.
r = 64.8 / 240 = o.27 = 27%.
To find the price of the notebook in Shop B, we need to do the following steps:
Step 1: Let's assume the price of the notebook in Shop B is x.
Step 2: We know that Shop A sold a notebook for $1200, which was 125% of the price in Shop B. So we can set up the equation:
1200 = 1.25x
Step 3: Now, we need to solve this equation to find the value of x. Divide both sides of the equation by 1.25:
x = 1200 / 1.25
x = 960
Therefore, the price of the notebook in Shop B is $960.
Now let's move on to the second part of the question to find the percentage discount given during the sale:
Step 1: We know that Dennis bought the notebook from Shop B and paid $175.20 less than the discounted price in Shop A.
Step 2: Let's assume the discounted price in both shops is y.
Step 3: We can set up the equation using the information given:
y - 175.20 = x
Step 4: We already found that the price of the notebook in Shop B is $960, so we can substitute this value into the equation:
y - 175.20 = 960
Step 5: Now, we need to solve this equation to find the discounted price y. Add 175.20 to both sides of the equation:
y = 960 + 175.20
y = 1135.20
Therefore, the discounted price in both shops is $1135.20.
Now, to find the percentage discount, we can calculate the difference between the original price and the discounted price, and then calculate the percentage:
Percentage discount = ((original price - discounted price) / original price) * 100
Percentage discount = (1200 - 1135.20) / 1200 * 100
Percentage discount = 64.80 / 1200 * 100
Percentage discount ≈ 5.4%
Therefore, the percentage discount given during the sale is approximately 5.4%.