Question

A construction worker has two different types of cement mixes. He needs to make

10 tons of concrete that is 40% cement by mixing a 20% cement mixture with a 70% cement
mixture. How much of each mixture does the construction worker need to use?

Answer 1

Answer; 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

Explanation: