1. ## Blending Teas

The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for 5 dollars per pound with some Orange Pekoe tea that sells for 3 dollars per pound to get 100 pounds of the new blend. The selling price of the new blend is to be four dollars and 50 cents per pound, and there is no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?

Let x = number of pounds required for each tea

5x + 3(100 - x) = 100(4.50)

Is this the correct set ?

2. ## Re: Blending Teas

Originally Posted by harpazo
The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for 5 dollars per pound with some Orange Pekoe tea that sells for 3 dollars per pound to get 100 pounds of the new blend. The selling price of the new blend is to be four dollars and 50 cents per pound, and there is no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?

Let x = number of pounds required for each tea

5x + 3(100 - x) = 100(4.50)

Is this the correct set ?
The formula is correct, but you described $x$ incorrectly. You say that it is the number of pounds required for each tea. In reality, you set it to be the number of pounds of the Earl Grey tea. You set $100-x$ to be the number of pounds for the Orange Pekoe. Other than that, it looks good. It is just your description of what $x$ means that can use some work.

3. ## Re: Blending Teas

Originally Posted by harpazo
The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for 5 dollars per pound with some Orange Pekoe tea that sells for 3 dollars per pound to get 100 pounds of the new blend. The selling price of the new blend is to be four dollars and 50 cents per pound, and there is no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?

Let x = number of pounds required for each tea
This is the same mistake you made in "financial planning"! You cannot set a single variable, x, to represent two values. In the equation you have below, x, because it is multiplied by 5, must be the number of pounds of Earl Gray tea. The "100- x" must be the number of pounds of Orange Pekoe.

5x + 3(100 - x) = 100(4.50)

Is this the correct set ?
You should have said "Let x= number of pounds of Earl Gray tea required". Then it would be a good idea to say "since we require a total of 100 pounds of tea, the number of pounds of Orange Pekoe required is 100- x".

4. ## Re: Blending Teas

5x + 3(100 - x) = 100(4.50)

5x + 300 - 3x = 450

2x = 450 - 300

2x = 150

x = 150/2

x = 75

The amount of pounds for Earl Grey tea is 75.

The amount of pounds for Orange Pekoe tea is 100 - 75 or 25 pounds.

5. ## Re: Blending Teas

Yes, that is correct. And it is easy to check yourself. First 25+ 75= 100 so you do have 100 pounds of tea. Further, 75 pounds of Earl Grey tea, at $5.00 a pound, would cost 5(75)=$375.00 while 25 pounds of Orange Pekoe, at $3.00$ a pound, would cost 3(25)= $75. That is a total of$450 for 100 pounds of tea- \$4.50 per pound as required.

6. ## Re: Blending Teas

I think the best thing for me to do is to read word problems several times, try to logically come up with the right equation and then post my solution equation here to see if it is correct or not. If my set up is incorrect, then correction is needed explaining what I did wrong.

7. ## Re: Blending Teas

Originally Posted by harpazo
I think the best thing for me to do is to read word problems several times, try to logically come up with the right equation and then post my solution equation here to see if it is correct or not. If my set up is incorrect, then correction is needed explaining what I did wrong.
GOOD thinking!

8. ## Re: Blending Teas

I posted 3 new word problems today. Please, let me know if my set up is correct. I will take it from there and show my complete work.