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How many kilograms of each type of tea must be used in the blend? A tea shop owner...

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spock5 | Student, Undergraduate | (Level 1) Honors

Posted May 14, 2012 at 4:15 AM via web

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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?

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

Posted May 14, 2012 at 4:33 AM (Answer #1)

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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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