Question

A store owner wishes to make a new tea with a unique flavor by mixing black tea and oolong tea. If he has 35 pounds of oolong tea that sells for $2.40 per pound, how much black tea worth $1.80 per pound must he mix with it so that he can sell the final mixture for $2.10 per pound?

Answer 1

Explanation:

Let's assume the store owner needs to mix x pounds of black tea with the 35 pounds of oolong tea.

The cost of the oolong tea is $2.40 per pound, so the total cost of the oolong tea is:

Cost of oolong tea = 35 pounds × $2.40/pound = $84

The cost of the black tea is $1.80 per pound, and the final mixture needs to be sold for $2.10 per pound. To achieve an average price of $2.10 per pound, the total cost of the mixture should be:

Total cost of mixture = (35 + x) pounds × $2.10/pound = $73.5 + $2.10x

Since the cost of the mixture should equal the sum of the costs of the oolong and black teas, we can set up the equation:

$73.5 + $2.10x = $84

Now, let's solve for x to find the amount of black tea needed:

$2.10x = $84 - $73.5

$2.10x = $10.5

x = $10.5 / $2.10

x ≈ 5

Therefore, the store owner needs to mix approximately 5 pounds of black tea with the 35 pounds of oolong tea in order to sell the final mixture for $2.10 per pound.

Answer 2

Explanation:

To solve this problem, we can use the following formula:

(quantity of tea 1 x price of tea 1) + (quantity of tea 2 x price of tea 2) = total quantity x price of mixture

Let x be the number of pounds of black tea that the store owner needs to mix with the oolong tea.

We know that:

The store owner has 35 pounds of oolong tea that sells for $2.40 per pound.

The store owner wants to sell the final mixture for $2.10 per pound.

The black tea is worth $1.80 per pound.

Using the formula above, we can write:

(35 x 2.40) + (x x 1.80) = (35 + x) x 2.10

Simplifying this equation, we get:

84 + 1.8x = 73.5 + 2.1x

0.3x = 10.5

x = 35

Therefore, the store owner needs to mix 35 pounds of black tea with the oolong tea.

I hope this helps! Let me know if you have any other questions.