Question

If $\frac{a}{b} = \frac{4}{3}$ and $3a + 2b = 24$, then find the value of $a$.

• A. 5
• B. 13/3
• C. 4
• D. 16/3

Answer 1

Answer:

D. 16/3

The value of $a$ is $\frac{16}{3}$ (or $5\frac{1}{3}$).

## Step 1: Express $b$ in terms of $a$

From the given ratio:

$\frac{a}{b} = \frac{4}{3}$

Cross-multiply to isolate $b$:

$3a = 4b \implies b = \frac{3a}{4}$

## Step 2: Substitute $b$ into the second equation

Substitute $b = \frac{3a}{4}$ into $3a + 2b = 24$:

$3a + 2\left(\frac{3a}{4}\right) = 24$

$3a + \frac{3a}{2} = 24$

## Step 3: Solve for $a$

Find a common denominator to add the terms on the left side:

$\frac{6a + 3a}{2} = 24$

$\frac{9a}{2} = 24$

$9a = 48$

$a = \frac{48}{9}$

Simplify the fraction by dividing both the numerator and the denominator by 3:

$a = \frac{16}{3}$