Question

8. Corey combines x pounds of

herbal tea at $12 per pound with
8 pounds of regular tea at $9 per
pound. He makes a mixture that
averages $10.50 per pound. Write
an equation to model the situation.

Answer 1

`12x+72=10.50(x+8)`

Explanation:

Cost of 1 pound of herbal tea = $12

Cost of x pounds of herbal tea = 12x

Cost of 1 pound of regular tea = $9

Cost of 8 pounds of regular tea =
`9* 8 = 72`

Now we are given that He makes a mixture that averages $10.50 per pound.

Total weight of mixture = 8 punds + x pounds = x+ 8

So,
`12x+72=10.50(x+8)`

Hence an equation to model the situation is
`12x+72=10.50(x+8)`

Answer 2

For this case we have to:

x: Let the variable representing the pounds of herbal tea

y: Let the variable representing the pounds of the mixture

According to the data we have:

`x + 8 = y`

On the other hand, to find the cost of each type of tea it is necessary to multiply the cost per pound, by the amount of pounds of each type of tea, that is:

`12x + 9 (8) = 10.50y\\12x + 72 = 10.50y`

Thus, we have the following system of equations:

`x + 8 = y\\12x + 72 = 10.50y`

Substituting the first equation in the second we have:

`12x + 72 = 10.50 (x + 8)`

ANswer:

The situation can be modeled by the following equation:

`12x + 72 = 10.50 (x + 8)`