Question

A merchant blends tea that sells for $3 an ounce with tea that sells for an ounce to produce 80 oz of a mixture that sells foran ounce. How many ounces of each type of tea does the merchant use in the blend?

Short answer

The ounces of $3 tea is 48 and the ounce of $2.75 tea is 32.

Step-by-step solution

Step-1. Determine the equations.

Let x be the amount of $3 tea and y be the amount of $2.75 tea.

Thus,$3x+2.75y=2.90\times 80\mathrm{...}\text{(1)}$

Also, the total amount is 80.

$x+y=80\mathrm{...}\text{(2)}$

Step-2. Use the equation.

Multiply the second equation by –3 and add the two equations.

$\begin{array}{l}3x+2.75y-3x-3y=232-3\left(80\right)\\ -0.25y=-8\\ y=32\end{array}$

Step-3. Substitute the value of y into the equation 2.

$\begin{array}{l}x+32=80\\ x=48\end{array}$

Hence, the ounces of $3 tea is 48 and the ounce of $2.75 tea is 32.