Question

A tea merchant mixes tea costing $7.40 per kg with tea costing $8.90 per kg in the ratio 3:2. At what price must he sell the mixture to make a profit of 15%?

Answer 1

The tea merchant must sell the mixed tea at $12.60 per kg to achieve a 15% profit, after calculating the cost per kg of the mixture using the given ratio and adding the profit margin.

Step-by-step explanation:

To determine the selling price of the tea mixture for a profit of 15%, we first calculate the cost per kg of the mixture using the given ratio and tea prices. We add the cost of the two types of tea proportionally: 3 parts at $7.40 per kg and 2 parts at $8.90 per kg. This calculation gives us the combined cost per kg of the mixture. Then we add a 15% profit margin to find the selling price.

First, we find the combined cost for 1 kg of the mixture:

• (3 parts * $7.40/kg) + (2 parts * $8.90/kg) = $37.00 + $17.80 = $54.80
• Total parts = 3 + 2 = 5 parts
• Cost per kg of mixture = $54.80 / 5 parts = $10.96 per kg

Now, we add a 15% profit margin to the cost:

• Profit margin = 15% of $10.96 = 0.15 * $10.96 = $1.644
• Selling price = Cost per kg + Profit margin = $10.96 + $1.644 = $12.604

The tea merchant must sell the mixture at $12.604 per kg (rounding to the nearest cent, $12.60 per kg) to achieve a 15% profit.