A furniture shop bought a table from the manufacturer and marked up the purchase price by 50%. At the Augustus Homemaker Sale, the price was reduced by 25%. The buyer saved 30$ on the price tag shown in the shop.
What did the shop pay the manufacturer for the table in the first place?
Did the furniture make a profit or a loss and by how much?
If the manufacturer price was $x, then
the store retail was 1.50x
At the sale, the price was 0.75 * 1.50x = 1.125x
The buyer paid 1.125x - 30
Since there are no real numbers given, it's impossible to answer the questions just now.
To find the original price the furniture shop paid the manufacturer for the table, we can follow these steps:
Step 1: Let's assume the purchase price from the manufacturer is X (in dollars).
Step 2: The shop marked up the purchase price by 50%. This means they increased it by 50% of X, which is 0.5X.
Step 3: So, the price tag shown in the shop is X + 0.5X, which equals 1.5X.
Step 4: At the Augustus Homemaker Sale, the price was reduced by 25%. This means the reduction is 25% of 1.5X, which is 0.25 * 1.5X = 0.375X.
Step 5: According to the question, the buyer saved $30 on the price tag shown in the shop. So, we can set up the following equation: 0.375X = $30.
Step 6: Now, we can solve the equation for X. Dividing both sides of the equation by 0.375, we get X = $30 / 0.375.
Calculating X, we find that X = $80.
Therefore, the shop paid the manufacturer $80 for the table in the first place.
To determine if the shop made a profit or a loss, we compare the original price the shop paid the manufacturer ($80) with the selling price after the discount.
The selling price after the discount is 75% of the marked-up price (1.5X). So, the selling price is 0.75 * 1.5X = 1.125X.
Comparing the shop's cost price ($80) with the selling price (1.125X), we can calculate the difference:
Profit/Loss = Selling Price - Cost Price
Profit/Loss = 1.125X - $80
Substituting X = $80, we get:
Profit/Loss = 1.125 * $80 - $80
Profit/Loss = $90 - $80
Profit/Loss = $10
Therefore, the furniture shop made a profit of $10 on the table.