In a departmental store, bags were sold at $40 each. During a sale, the bags were sold at a discounted price. As a result, the number of bags sold increased by60% and the total amount of money collected increased by 44%.(a) What was the price of a bag sold during the sale?(b)What was the percentage discount given for each bag during the sale?
Let the original number of bags be b
new number of bags after the discount= 160/100b =1.6b
total price for b bags before discount= 40b
100%=40b
144%=??
144/100×40b
=57.6b this is the price after the discount
price of each bag during sale= 57.6b/1.6b
=$36
(b)
discount=40-36
=$4
%discount= 4/40×100
=10%
To find the answers, we can follow these steps:
Step 1: Calculate the total number of bags sold before the sale.
Let's assume the initial number of bags sold before the sale was "x".
Step 2: Calculate the total number of bags sold during the sale.
Given that the number of bags sold increased by 60%, the new total number of bags sold can be expressed as:
Total number of bags sold during the sale = x + 60%x
Step 3: Calculate the original total amount collected from selling the bags.
The original total amount collected from selling the bags is:
Original total amount collected = Number of bags sold before the sale × Price of each bag = x × $40
Step 4: Calculate the increased total amount collected during the sale.
Since the total amount collected increased by 44%, the new total amount collected can be expressed as:
Increased total amount collected = Original total amount collected + 44% of Original total amount collected
= Original total amount collected + (44/100) × Original total amount collected
Step 5: Equate the increased total amount collected with the new price of each bag multiplied by the new total number of bags sold.
This can be expressed as:
Increased total amount collected = New price of each bag × New total number of bags sold
Step 6: Solve the equation obtained in step 5 to find the new price of each bag.
Step 7: Calculate the percentage discount given for each bag during the sale using the difference between the original price and the sale price.
Let's perform these calculations:
Step 1:
Let's assume the initial number of bags sold before the sale was "x".
Step 2:
Total number of bags sold during the sale = x + 60%x = x(1 + 0.6) = 1.6x
Step 3:
Original total amount collected = Number of bags sold before the sale × Price of each bag = x × $40 = $40x
Step 4:
Increased total amount collected = Original total amount collected + (44/100) × Original total amount collected
= $40x + (44/100) × $40x
= $40x(1 + 0.44)
= $40x(1.44)
Step 5:
Increased total amount collected = New price of each bag × New total number of bags sold
$40x(1.44) = New price of each bag × 1.6x
Step 6:
New price of each bag = ($40x(1.44))/(1.6x)
= $28.8
Step 7:
Percentage discount given for each bag during the sale = (Original price - Sale price) / Original price × 100
= ($40 - $28.8) / $40 × 100
= 28%
(a) The price of a bag sold during the sale was $28.8.
(b) The percentage discount given for each bag during the sale was 28%.
To solve this problem, we can break it down into two parts:
(a) Finding the price of a bag sold during the sale:
Let's assume the original number of bags sold before the sale is "x".
1. The number of bags sold during the sale increased by 60%, so the new number of bags sold is 1.6x (since 60% of x is 0.6x, and adding this to x gives 1.6x).
2. The total amount of money collected increased by 44%, which means the sale revenue is 1.44 times the original revenue.
Now, let's calculate the original revenue and the sale revenue:
- Original revenue = Original price per bag * Original number of bags sold = $40x
- Sale revenue = Sale price per bag * New number of bags sold = Sale price per bag * 1.6x
We know that the sale revenue is 1.44 times the original revenue, so we can equate the two expressions:
Sale revenue = 1.44 * Original revenue
Sale price per bag * 1.6x = 1.44 * ($40x)
Simplifying the equation:
Sale price per bag = (1.44 * $40) / 1.6 = $36
Therefore, the price of a bag sold during the sale is $36.
(b) Finding the percentage discount given for each bag during the sale:
The percentage discount is calculated by finding the difference between the original price and the sale price, divided by the original price, and then multiplied by 100.
Percentage discount = ((Original price per bag - Sale price per bag) / Original price per bag) * 100
Substituting the given values:
Percentage discount = (($40 - $36) / $40) * 100 = (4 / 40) * 100 = 10%
Therefore, the percentage discount given for each bag during the sale is 10%.
If n bags were sold at a discount price of p, then
1.60n*p = 1.44 * 40n
p = $36, so a 10% discount