Solve for t in the equation \(\frac{3}{4}\)t + \(\frac{1}{3}\)(21 - t) = 11
A
\(\frac{9}{13}\)
B
\(\frac{7}{13}\)
C
5
D
9\(\frac{3}{5}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{3}{4}\) t + \(\frac{1}{3}\) (21 - t) = 11
Multiply through by the LCM of 4 and 3 which is 12
12 x(\(\frac{3}{4}\) t) + 12 x (\(\frac{1}{3}\) (21 - t)) = (11 x 12)
9t + 4(21 - t) = 132
9t + 84 - 4t = 132
5t + 84 = 132
5t = 132 - 84 = 48
t = \(\frac{48}{5}\)
t = 9 \(\frac{3}{5}\)
Answer is D
Source: Myschool Past Questions Archive (Record #46984)