A tea wholesaler blends together three types of tea that normally sell for $10, $11 and
$12 per kilogram so as to obtain 100 kilograms of tea worth $11.20 per kilogram. If the
same amounts of the two higher priced teas are used, calculate how much of each type
must be used in the blend.

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sqdancefan sqdancefan · Answer 1 · 2021-12-31T03:30:32+01:00

Answer:

Step-by-step explanation:

Let x, y, z represent the quantities of 10, 11, and 12-dollar teas being used. We are given the relations ...

x + y + z = 100

10x +11y +12z = 11.20(100)

y = z

Using the last equation to substitute into the first two, we get two equations in two unknowns.

x + 2y = 100

10x +23y = 1120

Subtracting 10 times the first equation from the second gives ...

(10x +23y) -10(x +2y) = (1120) -10(100)

3y = 120

y = 40 . . . . . . divide by 3

Then z = 40, and x is ...

x = 100 -2y = 100 -2(40) = 20

20 kg of $10 tea, 40 kg of $11 tea, and 40 kg of $12 tea must be used.