SOLUTION: a contractor mixes concrete from bags of pre-mix for small jobs how many bags with 6% cement should he mix with 5 bags of 18.8% cement to produce a mix containing 10% cement?

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Question 1130150: a contractor mixes concrete from bags of pre-mix for small jobs how many bags with 6% cement should he mix with 5 bags of 18.8% cement to produce a mix containing 10% cement?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x bags of 6% cement
5 bags of 18.8% cement
want 10% cement

6x%2B%2818.8%29%285%29=10%28x%2B5%29
%2818.8%29%285%29-50=4x
x=%2818.8%2A5-50%29%2F4
x=11


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USING THE PERCENTS AS DECIMAL FRACTIONS AND SETUP WITH RATIONAL EXPRESSION

cement%2Fconcretemixture=fractionwanted


%280.06x%2B0.188%2A5%29%2F%28x%2B5%29=0.10
The algebra should be straightforward from here.

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

            Since the solution and the answer by @josgarithmetic are both   T O T A L L Y   W R O N G,  I came to fix it.

            Below find my correct solution.


x bags of 6% cement

5 bags of 18.8% cement

want 10% cement


    6x%2B%2818.8%29%285%29 = 10%28x%2B5%29     (*)


It is your basic equation to solve.


    18.8*5-50 = 4x

    x = %2818.8%2A5-50%29%2F4

    x = 11  bags of the 6% cement mix.       Answer


CHECK.  Left side of the equation (*)  0.06*11 + 0.188*5 = 1.6 is the pure cement amount

        Right side of the equation (*)  0.1*(11+5)       = 1.6 is the pure cement amount.    ! Both sides are equal  - the solution is 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
    - Advanced mixture problems
    - Advanced mixture problem for three alloys
    - OVERVIEW of lessons on word problems for mixtures
in this site.

A convenient place to quickly observe these lessons from a  "bird flight height"  (a top view)  is the last lesson in the list.

The most relevant of them is the lesson marked (*) in the list.

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.