SOLUTION: A 20-pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement? I think the equatio

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Question 1208989: A 20-pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement?

I think the equation should look like this:

%•amount + %•amount = %(mixture)
0.25(20) + 0.75(x) = 0.40(x + 20)
Is this correct?

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
A 20-pound bag of Economy brand cement mix contains 25% cement and 75% sand.
How much pure cement must be added to produce a cement mix that is 40% cement?

I think the equation should look like this:

%•amount + %•amount = %(mixture)
0.25(20) + 0.75(x) = 0.40(x + 20)
Is this correct?
~~~~~~~~~~~~~~~~~~~~~~~


        This is wrong.

        I will not explain, why it is wrong.

        I will write a correct solution, instead. 


Assume you add x pounds of pure cement.


Now the total mass is 20+x pounds; the portion of the pure cement is  0.25*20+x  pounds.


You want

    0.25*20 + x = 0.4*(20+x)  pounds.


It is your setup equation to solve and to find x.


Now I solve it for you step by step.  Watch my steps.


    5 + x = 8 + 0.4x,

    x - 0.4x = 8 - 5,

    0.6x = 3,

       x =  =  = 5 pounds  of the pure cement to add  (rounded).    ANSWER

Solved.



Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
A 20-pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement?


I think the equation should look like this:


%•amount + %•amount = %(mixture)

0.25(20) + 0.75(x) = 0.40(x + 20)

Is this correct? 

No, it's NOT.

Initial amount of cement (C): .25(20)
Amount of cement (C) to be added: 100%, or 1(C) 
Resulting CEMENT (C) in final mixture: .4(20 + C)

Cement + Cement = Cement
.25(20) + 1(C) = .4(20 + C) ===> .25(20) + C = .4(20 + C)

Now, solve for C, the amount of cement to be added.
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