Question

4. The density and strength of concrete are determined by the ratio of cement and aggregate. Suppose that a contractor has 480 cubic feet of a dry concrete mixture that is 70% sand by volume. How much pure sand must be added to form a new mixture that is 75% sand by volume?

Answer 1

The contractor needs to add 24 cubic feet of pure sand to the existing 480 cubic feet of dry concrete mixture, which is originally 70% sand by volume, in order to obtain a new mixture that is 75% sand by volume.

Step-by-step explanation:

To solve this problem, we can set up an equation based on the initial and final sand content and use the concept of density to find the total volume of sand in both scenarios. Since the contractor initially has 480 cubic feet of a dry concrete mixture that is 70% sand by volume, we can calculate the amount of sand in this initial mixture:

Initial sand content = 0.70 × 480 cubic feet = 336 cubic feetTo find out how much pure sand must be added to achieve a mixture that is 75% sand by volume, let's denote x as the amount of pure sand to be added. The new total volume of the mixture will be 480 + x cubic feet, and 75% of this new volume must be sand:

New sand content = 0.75 × (480 + x) cubic feet

Equating the initial sand content plus the pure sand added to the new sand content gives us:

336 + x = 0.75 × (480 + x)

Solving for x gives:

336 + x = 360 + 0.75x

x = 360 - 336

x = 24 cubic feet

Therefore, the contractor needs to add 24 cubic feet of pure sand to the dry concrete mixture to achieve a mixture that is 75% sand by volume.

Answer 2

The answer is 96ft^3

Step-by-step explanation:

T=initial concrete mixture

S1= initial amount of sand

S2=final amount of sand

T2=final amount concrete mixture

C=amount of cement

Data:

T=480Ft^3

the quantities of the initial mixture are

S=0.7*480=336Ft^3

C=0.3*480=144 Ft^3

we pose the following equations

144+S2=T2

T2*0.75=S2

if we solve

S2=144/(1/0.75-1)=432ft^3

to know how much we should add we subtract it from the initial amount of sand

Answer=432ft^3-336ft^3=96ft^3