I purchase 3kg of coffee and 2kg of tea for $76. There's a drought in South America causing the price of coffee beans and tea leaves to increase. Coffee prices increase by 20% and tea prices increase by 10%. I place the same order for coffee and tea yet this time I am charged $87.20. What are the original prices for 1kg of coffee and 1kg of tea? What are the new prices?

Original prices are $ 20 and $ 12 for tea and coffee respectively.

The new prices are $ 22 and $ 14.4 for tea and coffee respectively.

Step-by-step explanation:

Let C, the price of the original coffee and T be the precise of the original tea, we can pose the following equations:

First, the with the price of the initial values, since they give us the total value of the purchase.

3 * C + 2 * T = 76 (1)

Second, with the increased prices an equation can also be made because they give us the total value and the new price can be expressed as the function of the original price by the percentage increase, as follows:

3 * (1.2 * C) + 2 * (1.1 * T) = 87.2

Solving we have:

3.6 * C + 2.2 * T = 87.2

Reorganized:

C = (87.2 - 2.2 * T) / 3.6 (2)

Now, replacing (2) in (1) we are left with:

3 * [ (87.2 - 2.2 * T) / 3.6] + 2 * T = 76

Resolving

[ (3 * 87.2 - 3 * 2.2 * T) / 3.6] + 2 * T = 76

(261.6 - 6.6*T) / 3.6 + 2*T = 76

(261.6 - 6.6*T + 3.6*2*T) / 3.6 = 76

(261.6 + 0.6*T) / 3.6 = 76

261.6 + 0.6*T = 76*3.6

0.6*T = 273.6-261.6

T = (273.6-261.6) / 0.6

T = 20

Replacing in (2)

C = (87.2 - 2.2 * 20) / 3.6 = 12

Original prices are $ 20 and $ 12 for tea and coffee respectively.

The new prices would be:

1.2 * C = 1.2 * 12 = 14.4

1.1 * T = 1.1 * 20 = 22

Therefore, the new prices are $ 22 and $ 14.4 for tea and coffee respectively.