Question 1178773: in the tea shop they prepare a tea mixture with a price of 165 euros per kilogram. they will use cherry-flavored tea for EUR 250 per kilogram and apple tea 150 per kilogram to prepare this mixture. how many grams of tea they need to prepare one kilogram of mixture.
Found 3 solutions by mananth, greenestamps, josgarithmetic:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! x+y=1
250x+150y=165(x+y)
rearrange
15x-85y=0
let x grams cherry flavoured tea
y grams of apple tea
1.00 x + 1.00 y = 1.00
250.00 x + 150.00 y = 165.00 .............2
Eliminate y
multiply (1)by -150.00
Multiply (2) by 1.00
-150.00 x -150.00 y = -150.00
250.00 x 150.00 y = 165.00
Add the two equations
100.00 x = 15.00
/ 100.00
x = 0.15
plug value of x in (1)
1.00 x + 1.00 y = 1.00
0.15 + 1.00 y = 1.00
1.00 y = 0.85
y = 0.85
Ans x = 0.15
y = 0.85
150 grams cherry flavoured tea
850 grams of apple tea
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
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....
Let x = grams of apple tea at 150 EUR per kg
Then 1000-x = grams of cherry tea at 250 EUR per kg
The mixture is to be 1000 grams at 165 EUR per kg:
ANSWER: x=850 grams of apple tea, 1000-x=150 grams of cherry tea
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.
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.
Answer by josgarithmetic(39620)  (Show Source):
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