Question

A merchant blends tea that sells for $3.25 an ounce with tea that sells for $2.50 an ounce to produce 90 oz of a mixture that sells for $2.80 an ounce. How many ounces of each type of tea does the merchant use in the blend?

Answer 1

Answer: The amount of tea ounces that sells for $ 3.25 is 36, and the amount of tea ounces that sells for $ 2.50 is 54.

Step-by-step explanation:

We start by defining variables from the data provided:

a = amount of ounces of tea that sells for ​​$ 3.25

b = amount of ounces of tea that sells for ​​$ 2.50

c = amount of ounces of tea that sells for ​​$ 2.80

From the problem we know that $a + b = c$, and that $3.25 * a + 2.50 * b = 2.80 * c$. You can propose a system of equations:

$\left \{ {{a + b = c} \atop {3.25 * a + 2.50 * b = 2.80 * c}} \right.$

Having the fact that c = 90, we can simplify the system:

$\left \{ {{a + b = 90} \atop {3.25 * a + 2.50 * b = 252}} \right.$

Clearing a in the first equation we get:

$a = 90 - b$

And substituting in the second equation we arrive at:

$3.95 * (90 - b) * 2.50 * b = 252, we\ apply\ the\ distributive\ property\\ 292.5 - 3.25 * b + 2.50 * b = 252, add\ the\ terms\ containing\ b\\292.5 - 0.75 * b = 252, we\ subtract\ 292.5\ from\ both\ sides\\- 0.75 * b = -40.5, we\ divide\ by -0.75\\b = 54$

Now we can use b in the first equation to get a:

$a = 90 - b = 90 - 54 = 36$

We verify that $36 + 54 = 90$, and that $3.25 * 36 + 2.50 * 54 = 252$.