Question

A special blend of tea costs $15.70 per pound to make. It is made by combining herbs that cost $14.50 per pound with black tea that costs $16.90 per pound. To make a batch of this blended tea, how many pounds of black tea should be added to 14 pounds of herbs?

Answer 1

Let's define:

x: pounds of herbs

y: pounds of black tea

z: pounds of special blend tea

The special blend cost $15.70 per pound, the herbs cost $14.50 per pound, the black tea cost $16.90 per pound. That is,

15.70z = 14.50x + 16.90y

The blend is made by adding herbs and black tea, then:

x + y = z

Given that 14 pounds of herbs are added, then x = 14. Replacing this information into the second equation we get:

14 + y = z

Substituting the last equation and x = 14 into the first equation, we get:

15.70(14 + y) = 14.50*14 + 16.90y

15.70*14 + 15.70y = 203 + 16.90y

219.8 + 15.70y = 203 + 16.90y

219.8 - 203 = 16.90y - 15.70y

16.8 = 1.2y

16.8/1.2 = y

14 = y

14 pounds of black tea should be added to 14 pounds of herbs