Question:

Cement Mix?

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

Answer:

x+20(.25)=.40(x+20) x+5=.40x+8 Subtract .4x from both sides: .6x+5=8 Subtract 5 from both sides: .6x=3 Divide .6 from both sides: x=5 5 pounds of pure cement.
Let x = amount of pure cement (note that pure cement is 100% cement). You are given that 20 = amount of 25% cement. The new mixture (40% cement) will be x+20. Now insert the percentages. (100%)(x) + (25%)(20) = (40%)(x+20) 1x + 5 = 0.4x + 8 Subtract 0.4x from each side 0.6x + 5 = 8 Subtract 5 from each side 0.6x = 3 Divide both sides by 0.6 x = 3/0.6 x = 5 Answer: 5 pounds of pure cement

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