Question 1178773
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The response from tutor @mananth makes the problem look more complicated than it is.  The solution to a problem is always easier if you set it up using a single variable instead of two.  And why she chooses always to represent whole numbers with 2 decimal places is a mystery....<br>
Let x = grams of apple tea at 150 EUR per kg
Then 1000-x = grams of cherry tea at 250 EUR per kg<br>
The mixture is to be 1000 grams at 165 EUR per kg:<br>
{{{150(x)+250(1000-x) = 165(1000)}}}
{{{150x+250000-250x = 165000}}}
{{{85000 = 100x}}}
{{{x = 85000/100 = 850}}}<br>
ANSWER: x=850 grams of apple tea, 1000-x=150 grams of cherry tea<br>
If a formal algebraic solution is not required, and if the speed of obtaining a solution is important (as in a timed math competition), solution can be obtained very quickly with some logical reasoning and a bit of mental arithmetic.<br>
The cost per kg of the mixture, 165, is 15/100 of the way from 150 to 250, the costs per kg of the two ingredients (picture the three numbers 150, 165, and 250 on a number line, if it helps).
That means 15/100 of the mixture must be the more expensive ingredient.
ANSWER: 15/100 of 1000g, or 150g, of the cherry tea, the other 850g of apple tea.<br>