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?

The answer is 96ft^3

Explanation:

T=initial concrete mixture

S1 = initial amount of sand

S2=final amount of sand

T2=final amount concrete mixture

C=amount of cement

dа ta:

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