a) Let the numbers be 1/3x, 2/3x, and 3/4x. The sum of these numbers is 1/3x + 2/3x + 3/4x = 276. Combining like terms, we get 7/12x = 276. Multiplying both sides by 12/7, we find x = 504. Therefore, the numbers are (1/3)(504) = 168, (2/3)(504) = 336, and (3/4)(504) = 378.
b) Let the lengths of the pieces be 3x, 4x, and 5x. The sum of these lengths is 3x + 4x + 5x = 12x. Since the height of the tree is 4.8 m, we have 12x = 4.8. Dividing both sides by 12, we find x = 0.4. Therefore, the lengths of the pieces are 3(0.4) = 1.2 m, 4(0.4) = 1.6 m, and 5(0.4) = 2 m.
c) Since x : y = 7 and y : z = 15 : 7, we can find the ratio x : z by multiplying the two ratios together. (x : y) * (y : z) = 7 * (15/7) = 15. Therefore, x : z = 15.
d) Since a : b = 2 : 3 and b : c = 4 : 5, we can find the ratio a : b : c by multiplying the two ratios together. (a : b) * (b : c) = (2 : 3) * (4 : 5) = 8 : 15. Therefore, a : b : c = 8 : 15.