SOLUTION: How many kilograms of sand must be added to 300 kg of a mixture of sand and cement containing 40% cement to produce a mixture which will be 75% sand?

Question 1117131: How many kilograms of sand must be added to 300 kg of a mixture of sand and cement containing 40% cement to produce a mixture which will be 75% sand?
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
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How many kilograms of sand must be added to 300 kg of a mixture of sand and cement containing 40% cement to produce a mixture which will be 75% sand?
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The mixture containing 40% cement contains 60% of sand. So the question is How many kilograms of sand must be added to 300 kg of a mixture of sand and cement containing 60% of sand to produce a mixture which will be 75% sand? 0.60*300 + x = 0.75*(300+x) <<<---=== it is your basic balance equation 0.6*300 + x = 0.75*300 + 0.75x x - 0.75x = 0.75*300 - 0.6*300 0.25x = 0.15*300 ====> x = = 3*300/5 = 3*60 = 180. Answer. 180 kilogram of sand should be added. Check. = 0.75 = 75% is the final percentage of sand. ! Correct !

Solved.

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There is entire bunch of lessons covering various types of mixture problems
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Word problems on mixtures for antifreeze solutions
    - 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 (*)
    - Word problems on mixtures for alloys
    - Typical word problems on mixtures from the archive
    - OVERVIEW of lessons on word problems for mixtures
in this site.

There is even one (marked by (*) in the list) specially devoted to similar dry mixtures.
Read them and become an expert in solution the 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 online textbook 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 josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
The 300 kg mixture of 40% cement is 60% sand.

Adding x, kilograms of sand,

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

You have received two responses to your question, both using an algebraic solution using an equation for the amount of sand in the mixture:

"x kg of sand, plus 60% of 300 kg of mixture which is 60% sand, equals 75% of (x+300) kg of sand"

This of course is a valid approach to the problem. However, when one of the ingredients being mixed is 100% one thing and 0% the other, I find it easier to think in terms of the ingredient that is NOT being added.

For this problem, you start with 300 kg of a mixture which is 40% cement and 60% sand, and you are adding only sand to end up with a mixture that is 75% sand and only 25% cement.

(1) The cement in the original mixture is 40% of 300 kg, or 120 kg.
(2) When the additional sand is added to the mixture, that 120 kg is now only 25% of the mixture.
(3) So the total amount of mixture must now be 120/.25 = 480 kg.
(4) So the amount of sand that was added was 480-300 = 180 kg.
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