Solve for t in the equation $\frac{3}{4}$t + $\frac{1}{3}$(21 - t) = 11

Analysis

To solve for $t$ in the equation $\frac{3}{4}t + \frac{1}{3}(21 - t) = 11$, we need to clear the fractions, expand the brackets, and isolate the variable $t$.

Concept

When dealing with equations involving fractions, the easiest way to simplify them is to find the Least Common Multiple (LCM) of the denominators and multiply every term in the equation by that value. This eliminates the fractions and makes the equation much easier to solve.

Step-by-Step Solution

Step 1: Identify the LCM The denominators are 4 and 3. The LCM of 4 and 3 is 12.

Step 2: Multiply every term by 12 $12 \times (\frac{3}{4}t) + 12 \times (\frac{1}{3}(21 - t)) = 12 \times 11$

Step 3: Simplify the terms

• $12 \div 4 = 3$, so $3 \times 3t = 9t$
• $12 \div 3 = 4$, so $4 \times (21 - t) = 84 - 4t$
• $12 \times 11 = 132$

Now the equation looks like this: $9t + 84 - 4t = 132$

Step 4: Combine like terms $9t - 4t + 84 = 132$ $5t + 84 = 132$

Step 5: Isolate $t$ Subtract 84 from both sides: $5t = 132 - 84$ $5t = 48$

Divide by 5: $t = \frac{48}{5}$

Step 6: Convert to a mixed fraction $48 \div 5 = 9$ remainder $3$. So, $t = 9\frac{3}{5}$

Conclusion

Comparing our result to the given options, we find that $9\frac{3}{5}$ matches option D.

Exam Tip

When you have an equation with fractions, don't be tempted to work with decimals unless necessary. Clearing the fraction by multiplying by the LCM is a "golden rule" in JAMB Mathematics—it prevents errors that often occur when adding or subtracting fractions with different denominators.