SOLUTION: a grocer sells Brazilian coffee at R30 per kilogram and Colombian coffee at R51 per kilogram.calculate how many kilograms of each should he mix to have a blend of 50 kilograms that

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Question 1181173: a grocer sells Brazilian coffee at R30 per kilogram and Colombian coffee at R51 per kilogram.calculate how many kilograms of each should he mix to have a blend of 50 kilograms that he can sell at R42.60 per kilogram
Found 4 solutions by greenestamps, mananth, josgarithmetic, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


First a standard algebraic solution....

x kg at R30 per kg, plus (50-x) kg at R51 per kg, equals 50 kg at 42.60 per kg:

30%28x%29%2B51%2850-x%29=42.6%2850%29
30x%2B2550-51x=2130
-21x=-420
x=-420%2F-21=20

ANSWER: x=20kg of the Brazilian; 50-x=30kg of the Colombian.

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And now an easy path to the answer if a formal algebraic solution is not required....

Look at the three prices per kg on a number line -- 30, 42.60, and 51 -- and determine that 42.60 is 12.60/21 = 0.6 = 3/5 of the way from 30 to 51.

That means 3/5 of the mixture should be the higher priced Colombian coffee.

ANSWER: 3/5 of 50kg, or 30kg, of Colombian and the other 20kg of Brazilian.

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The explanation in words makes this look like a longer path to the answer than the formal algebra. However, the numbers you need to work with are much simpler with this informal solution method.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Type R ---------------- quantity
Brazilian coffee 30 ---------------- x kg
Columbian coffee 51 ---------------- 50 - x kg
Mixture 42.60 ---------------- 50

30 x + 51 ( 50 - x ) = 50.00 * 42.60

30 x + 2550 - 51 x = 2130.00
30 x - 51 x = 2130 - 2550
-21 x = -420
/ -21
x = 20 kg Brazilian coffee
30 kg Columbian coffee

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
L = R30, lower priced coffee
H = R51, higher priced coffee
x, how much of the higher priced coffee to use
M = 50 kilograms
M-x, quantity of lower priced coffee to use
T = R42.6, price of mixture

Hx%2BL%28M-x%29=TM, equation to account for the cost of the mixture.
Hx%2BLM-Lx=TM
Hx-Lx=TM-LM
%28H-L%29x=TM-LM
highlight%28x=%28TM-LM%29%2F%28H-L%29%29

Substitute the given values for M, T, H, and L. Evaluate x and M-x.

x=50%28%2842.6-30%29%2F%2851-30%29%29
.
.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

When students come to the forum with such problems,  they should learn  THE  LOGIC  of the solution,
and that is all what they should know.


The students should not know these formulas,  that  @josgarithmetic tries to sell you.


Even do not try to understand or memorize these formulas --- keeping them in your mind is absolutely useless
and will teach you to NOTHING.


THEREFORE,  for a sake of your safety,  ignore his post and do not load this  TRASH  into your head / (mind).


May god saves you from it . . .


Keep your mind clean for more useful/vital tasks of your life.