If x : y : z = 3 : 3 : 4, evaluate (frac{9x + 3y}{6z – 2y})
-
A.
1(frac{1}{2}) -
B.
2 -
C.
2(frac{1}{2}) -
D.
3
Correct Answer: Option A
Explanation
If x : y : z = 3 : 3 : 4, evaluate (frac{9x + 3y}{6x – 2y})
(frac{x}{y}) = (frac{2}{3}) and (frac{y}{z}) = (frac{3}{4})
Thus; x = (frac{2}{3}T_1) and z = (frac{3}{5}T_1)
y = (frac{3}{7}T_2) and z = (frac{4}{7}T_2)
Using y = y
(frac{3}{5}T_1) = (frac{3}{7}T_2); (frac{T_1}{T_2}) = (frac{3}{7}) x (frac{5}{3})
(frac{T_1}{T_2}) = (frac{15}{21})
(T_1) = 15 and (T_2) = 21
Therefore;
x = (frac{2}{5}) x 15 = 6
y = (frac{3}{5}) x 15 = 9
y = (frac{3}{7}) x 21 = 9 (again)
z = (frac{4}{7}) x 21 = 12
Hence;
(frac{9x + 3y}{6z – 2y}) = (frac{9(6) + 3(9)}{6(12) – 2(9)})
(frac{54 + 27}{72 – 18}) = (frac{81}{54}) = (frac{3}{2})
= 1(frac{1}{2})