A construction project requires 2400 bags of cement to be distributed among three sites X, Y, and Z in the ratio 3:4:5. a) Determine the fraction of the bags of cement that each site should receive. b) Calculate the number of cement bags each site should receive.

Uwiano wa tovuti X, Y, na Z ni $3:4:5$.
Jumla ya sehemu ni:

$$3 + 4 + 5 = 12$$

Sehemu ya tovuti X:

$$\frac{3}{12} = \frac{1}{4}$$

Sehemu ya tovuti Y:

$$\frac{4}{12} = \frac{1}{3}$$

Sehemu ya tovuti Z:

$$\frac{5}{12}$$

Sehemu ya mifuko ya saruji ambayo kila tovuti inapaswa kupokea ni:
Tovuti X: $\boxed{\frac{1}{4}}$
Tovuti Y: $\boxed{\frac{1}{3}}$
Tovuti Z: $\boxed{\frac{5}{12}}$

Idadi ya mifuko kwa tovuti X:

$$\frac{1}{4} \times 2400 = 600 \text{ mifuko}$$

Idadi ya mifuko kwa tovuti Y:

$$\frac{1}{3} \times 2400 = 800 \text{ mifuko}$$

Idadi ya mifuko kwa tovuti Z:

$$\frac{5}{12} \times 2400 = 5 \times 200 = 1000 \text{ mifuko}$$

Idadi ya mifuko ya saruji ambayo kila tovuti inapaswa kupokea ni:
Tovuti X: $\boxed{600 \text{ mifuko}}$
Tovuti Y: $\boxed{800 \text{ mifuko}}$
Tovuti Z: $\boxed{1000 \text{ mifuko}}$