Question 1044390: An amount of cement, sand, and gravel, mixed in the ratio 1-2-4 (1 part cement, 2 parts sand, 4 parts gravel) are needed to make 1 cu. yd. of solid concrete, allowing 33 1/3% voids (air spaces) in the sand and 45% voids in the gravel. Determine amount(cu. yds.) of each.
Solution provided with problem:
Let x = cu. yd. of cement.
Let y = cu. yd. of sand.
Let z = cu. yd. of gravel.
The voids are filled in finished concrete and the z cu. yd. count only as .55z cu. yd. of solid concrete, and the y cu. yd. of sand count only at 2/3y cu. yd. of gravel. No voids in the cement.
Equations:
(1) x + 2/3y + .55z = 1 (cu. yd. of concrete)
(2) y = 2x and z = 4x, from ratios in mixture.
Substituting values of y and z from (2) in (1),
x + 4x/3 + 2.2x = 1
Please explain solution.
Answer by ikleyn(52776)   (Show Source):
You can put this solution on YOUR website! .
I think that this scheme is infinitely far from reality.
And has nothing common with the reality.
So there is no sense to consider it and to try to solve.
Let us consider the equation (1) and, in particular, the term 0.55z.
It is z - 0.45z.
Do you assume that the gravel consolidates/compresses "inside itself" (implodes) to zeroes its own porosity ?
Same question about the addend  for sand.
Do you know that a significant amount of water is needed and is used to produce concrete ?
Where is the water in your balance ?
The mechanism and the scheme of forming concrete is much more complicated.
The scheme in this post/solution is totally inadequate.
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