How many kilograms of each type of tea must be used in the blend? A tea shop owner blends tea that sells for 240 pesos per kilo to another type of tea that sells for 200 pesos per kilo to produce...

How many kilograms of each type of tea must be used in the blend?

A tea shop owner blends tea that sells for 240 pesos per kilo to another type of tea that sells for 200 pesos per kilo to produce 150 kilos of a mixture that sells for 220 pesos. How many kilograms of each type of tea must be used in the blend?

Asked on by spock5

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thilina-g | College Teacher | (Level 1) Educator

Posted on

Let A be the tea that sells 240 pesos per kilo and Let B be the tea which sells 200 pesos per kilo. The amount taken from A is x and amount taken from B is y. Then,

Total amount = `150 = x+y`

Selling price of 150 kg `= 220(150) = 240x+200y`

Thereforem `220(150) = 240x+200y`

Dividing by 40,

`825 = 6x+5y`

Now e have two simultaneous equations for x and y, we can solve theme to fins values for x and y.

x = 75 and y =75.

The amount needed from each type are, 75 kg from A and 75 kg from B.

Now let us check our answer.

Cost of 150 kg of mixture  = 75(240)+75(200)

                                       = 33000

Cost of 1 kg of mixture      = 33000/150

                                       = 220.

Therefore our answer is correct.

 

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