Intermediate Algebra, Chapter 2, 2.3, Section 2.3, Problem 62

Lee Ann Spahr wants to mix tea worth $2$ cents per oz with $100$ oz of tea
worth $5$ cents per oz to make a mixture worth $3$ cents per oz. How much $2$ cents tea should be used?

Step 1: Read the problem, we are asked to find the quantity of $2$ cents tea in the solution.
Step 2 : Assign the variable. Then organize the information in the table.
Let $x =$ quantity of $2$ cents tea.


$\begin{array}{|c|c|c|c|c|c|} \hline & \text{Ounces of Tea} & \cdot & \text{Cost per Ounce} & = & \text{Total Cost} \\ \hline 2 \text{cents} & x & \cdot & 0.02 & = & 0.02x \\ \hline 5 \text{cents} & 100 & \cdot & 0.05 & = & 0.05(100) \\ \hline 3 \text{cents} & x + 100 & \cdot & 0.03 & = & 0.03(x + 100) \\ \hline \end{array}$

The sum of the quantities of each solution is equal to the quantity of the resulting solution

Step 3: Write an equation from the last column of the table
$0.02x + 0.05(100) = 0.03(x + 100)$

Step 4: Solve

$\begin{equation} \begin{aligned} 0.02x + 5 &= 0.03x + 3\\ \\ 0.02x - 0.03x &= 3 - 5\\ \\ -0.01x &= -2 \\ \\ x &= 200 \end{aligned} \end{equation}$


Step 5: State the answer
In other words, $200$ oz of $2$ cents tea must be used.