Question

If $\frac{a}{3}$ = $\frac{b}{2}$, then find the value of the ratio $\frac{5a+3b}{7a-2b}$.
$\left[3\right]$

Answer 1

Solution:
Let $\frac{a}{3}$ = $\frac{b}{2}$ = t [1 Mark]

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∴ Substituting a = 3t and b = 2t, we get

$\frac{5a+3b}{7a-2b}$ = $\frac{5\left(3t\right)+3\left(2t\right)}{7\left(3t\right)-2\left(2t\right)}(t\ne 0)$ [1 Mark]

= $\frac{15t+6t}{21t-4t}$

= $\frac{21t}{17t}$

= $\frac{21}{17}$. [1 Mark] <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}-->