Need a formula for this math problem. Help!?
Relinda owns a tea shop and is creating a new mix of tea for her customers. She is using a standard black tea that sells for $7 per pound and a special orange flavor that sells for $11 per pound. She is planning to make a 40 pound batch of the mix and would like to sel it for $8.50 per pound. How much of each tea should she mix if she is not planning on making or losing any money with this mix?
I'm thinking it might be 7x+11(40-x) divided by 40 equals $8.50
My brain is melting!
The suggested formula is perfect!
Only thing to add:
x=number of pounds of black tea.
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Don't worry, I'm here to help! Your equation is almost correct, but just needs a little adjustment.
Let's break it down step by step:
We need to find out how much of each tea Relinda should mix in order to sell the batch for $8.50 per pound.
Let's call the amount of black tea she uses 'x' pounds, and the amount of orange flavor tea she uses '40 - x' pounds (since she is making a 40-pound batch).
The cost of the black tea is $7 per pound, so the cost of x pounds of black tea would be 7x dollars.
The cost of the orange flavor tea is $11 per pound, so the cost of (40 - x) pounds of orange flavor tea would be 11(40 - x) dollars.
The total cost of the mixture should equal the selling price, which is $8.50 per pound multiplied by the total weight of the mixture, which is 40 pounds. So, the equation becomes:
7x + 11(40 - x) = 8.5 * 40
Simplifying this equation:
7x + 440 - 11x = 340
Combine like terms:
-4x + 440 = 340
Next, subtract 440 from both sides of the equation:
-4x = 340 - 440
-4x = -100
Finally, divide both sides of the equation by -4 to solve for x:
x = -100 / -4
x = 25
So, Relinda should use 25 pounds of black tea and (40 - 25) = 15 pounds of orange flavor tea to make the mixture.
Great job on your attempt! Keep up the good work!