SOLUTION: How many grams of soil supplement that cost P280 per kilogram must be mixed with 20 kg of aluminum nitrate that costs P140 per kilogram to make a fertilizer that P180 per kilogram?

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Question 1173323: How many grams of soil supplement that cost P280 per kilogram must be mixed with 20 kg of aluminum nitrate that costs P140 per kilogram to make a fertilizer that P180 per kilogram?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

The setup is this equation


    280x + 20*140 = 180(x+20).


From the equation,


    x =  = 8.


ANSWER.  8 kilograms.

Solved.

---------------

It is a standard and typical mixture problem.

For introductory lessons covering various types of mixture word problems see
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Typical word problems on mixtures from the archive
    - Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts
    - Word problems on mixtures for dry substances like candies, dried fruits
    - Word problems on mixtures for dry substances like soil and sand
in this site.

You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization,  from very detailed to very short.

Read them and become an expert in solution mixture word problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook in the section "Word problems" under the topic "Mixture problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


If a formal algebraic solution is not required, here is a quick and easy way to solve the problem with a bit of mental arithmetic.

The prices per kg of the two ingredients are P140 and 280; the price per kg of the mixture is P180.

180 is 40/140 = 4/14 = 2/7 of the way from 140 to 280 (look at the three numbers on a number line, if it helps).

That means 2/7 of the mixture is the more expensive ingredient and 5/7 of the mixture is the less expensive.

So the amount of soil supplement that must be added is (2/7)/(5/7) = 2/5 of the amount of aluminum nitrate.

ANSWER: (2/5)(20) = 8kg = 8000g

CHECK:
(20)(140)+8(280) = 2800+2240 = 5040
28(180) = 5040
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