21. How many pounds of tea that cost S4.20 per pound must be mixed with 12 lb of tea that cost S2.25 per pound to make a mixture that costs S3.40 per pound?


Let's denote the number of pounds of the tea that costs $4.20 per pound as $ x $.

### Step 1: Set up the equation
The total cost of the mixture is given by the equation:

\[
\text{Total cost} = \text{Cost of first tea} + \text{Cost of second tea}
\]

\[
(4.20 \times x) + (2.25 \times 12) = 3.40 \times (x + 12)
\]

### Step 2: Simplify and solve the equation
First, calculate the cost of the 12 pounds of the second type of tea:

\[
2.25 \times 12 = 27
\]

So the equation becomes:

\[
4.20x + 27 = 3.40(x + 12)
\]

Expand and simplify the right side of the equation:

\[
4.20x + 27 = 3.40x + 40.8
\]

Next, subtract $ 3.40x $ from both sides:

\[
0.80x + 27 = 40.8
\]

Then, subtract 27 from both sides:

\[
0.80x = 13.8
\]

Finally, divide by 0.80 to find $ x $:

\[
x = \frac{13.8}{0.80} = 17.25
\]

### Final Answer
You need to mix **17.25 pounds** of the tea that costs $4.20 per pound with 12 pounds of the tea that costs $2.25 per pound to get a mixture that costs $3.40 per pound.

Would you like more details or have any questions? Here are some related questions:

1. What if the desired mixture cost was $3.50 per pound instead?
2. How would the solution change if the amount of the cheaper tea was different?
3. Can this problem be solved using a different method, such as weighted averages?
4. What is the significance of ensuring the cost per pound in mixtures?
5. How does this problem relate to concepts in linear equations?

**Tip:** Always verify your final answer by substituting it back into the original equation to check if it satisfies all conditions.

Learn how to solve a mixture problem involving different costs of tea. Find out how many pounds of tea that costs $4.20 per pound need to be mixed with 12 pounds of tea costing $2.25 per pound to achieve a mixture costing $3.40 per pound. Detailed step-by-step solution provided.

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