How concentrated is my tea?

Number Theory Level pending

Two kinds of tea worth $ 126 kg \$126\text{kg} and $ 135 kg \$135\text{kg} are mixed with another kind of tea in the ratio 1 : 1 : 2 1:1:2 .

If the mixture is worth $ 153 kg \$153 \text{kg} .

Find the price of third variety (answer your answer per 1 kg 1 \text{kg} ).

Picture Source File: Wikimedia

175.5 189.75 170 176.5

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1 solution

Venture Hi
Mar 3, 2015

Since their ratio is 1:1:2, we can conclude that the mixture contains a kg of the $126/kg variety, 1 kg of the $135/kg variety and 2 kg of the $X/kg variety. The mixture of these 3 varieties cost $153/kg Hence, (126+135+2x)/4=153 x=$175.5

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