A merchant marks a certain lamp up 30% above cost.then he gives a customer a 15% discount.if the final selling price of the lamp was $99,what was the approximate cost price?
after a 30% markup the price is cost * 1.30
After a 15% discount, the price is
cost * 1.30 * 0.85 = cost * 1.105
That price is $99, so
1.105 * cost = 99
cost = 99/1.105 = 89.59
cost * 1.30 * (1-0.15) = 99
cost = 99/1.105 = 89.59
didnt get the answer..can u explain pls??
To find the approximate cost price of the lamp, we need to follow these steps:
Step 1: Calculate the selling price after the 30% markup.
To do this, let's assign a variable to the cost price of the lamp. Let's call it "x". Since the merchant marks up the lamp by 30%, the selling price before the discount can be calculated as:
Selling price before discount = x + (30/100) * x
Step 2: Calculate the selling price after the 15% discount.
Since the customer receives a 15% discount, the selling price after the discount is calculated as:
Selling price after discount = Selling price before discount - (15/100) * Selling price before discount
Step 3: Set up an equation using the given information.
The problem states that the final selling price of the lamp was $99. Thus, we can set up the following equation:
99 = Selling price after discount
Step 4: Solve the equation.
Substitute the values obtained in Step 1 and Step 2 into the equation from Step 3, and solve for "x".
99 = (x + (30/100) * x) - (15/100) * (x + (30/100) * x)
Now, we simplify the equation:
99 = x + 0.3x - 0.15x - 0.045x
Combining like terms:
99 = x + 0.155x
Combining the coefficients of "x":
99 = 1.155x
Dividing both sides by 1.155:
99/1.155 = x
x ≈ 85.71
Hence, the approximate cost price of the lamp is approximately $85.71.