In a department store, the total cost of the 30 audio systems, S51000. If each audio system is sold at 15% off, the department store will make a profit of 25%. Find marked price of each audio system.
Let's start by calculating the total cost of the 30 audio systems.
Total cost = 30 * Cost per audio system = S51000
Therefore, Cost per audio system = S51000 / 30 = S1700
Let's assume the marked price of each audio system is M.
If each audio system is sold at 15% off, the selling price of each audio system will be 85% of the marked price.
Selling price = 85% of M = 0.85M
According to the given information, the department store will make a profit of 25% on the cost price.
Profit = Selling price - Cost price
Profit = 0.25 * Cost price
Since we know the cost price of each audio system is S1700, we can write:
Profit = 0.25 * 1700 = S425
Now, we can write the equation for profit as:
Profit = Selling price - Cost price
425 = 0.85M - 1700
Solving for M, we get:
0.85M = 425 + 1700
0.85M = 2125
M = 2125 / 0.85
M = 2500
Therefore, the marked price of each audio system is S2500.