20lb cement adds cement to create 40%cement

Question

A 20lb bag of economy brand cement contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mixture that is 40% cement?

Answer 1

Hi Viktoria,

 

Let's begin by assigning a letter to represent our unknown:

    x = # ibs. of input pure (100%) cement

 

Now let's write expressions for the amount of cement contained in each bag:

    (20)(0.25) = # lbs. of input 25% cement

    (x)(1.00) = # lbs of input pure (100%) cement

    (20 + x)(0.40) = # lbs. of output 40% cement

 

Next, we'll write an equation to express the mixing our two input bags to produce our output bag and solve that equation for our unknown (x):

    (20)(0.25) + (x)(1.00) = (20 + x)(0.40)

    5 + x = (20)(0.40) + 0.4x

    5 + x = 8 + 0.4x

    x - 0.4x = 8 - 5

         0.6x = 3

             x = 3/0.6

             x = 5 lbs. of input pure (100%) cement

 

Finally, we can check our answer by plugging it back into our equation to see if the sum of the inputs is equal to the output:

    (20)(0.25) + (x)(1.00) = (20 + x)(0.40)

    (20)(0.25) + (5)(1.00) = (20 + 5)(0.40)

    5 + 5 = (25)(0.40)

        10 = 10 (sum of inputs = output)

 

Since the sum of our input cement amounts is equal to the output cement amount, we are confident that our answer is correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.