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 [tex]a + b = c[/tex], and that [tex]3.25 * a + 2.50 * b = 2.80 * c[/tex]. You can propose a system of equations:
[tex]\left \{ {{a + b = c} \atop {3.25 * a + 2.50 * b = 2.80 * c}} \right.[/tex]
Having the fact that c = 90, we can simplify the system:
[tex]\left \{ {{a + b = 90} \atop {3.25 * a + 2.50 * b = 252}} \right.[/tex]
Clearing a in the first equation we get:
[tex]a = 90 - b[/tex]
And substituting in the second equation we arrive at:
[tex]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[/tex]
Now we can use b in the first equation to get a:
[tex]a = 90 - b = 90 - 54 = 36[/tex]
We verify that [tex]36 + 54 = 90[/tex], and that [tex]3.25 * 36 + 2.50 * 54 = 252[/tex].
