Rani has 36 red balloons and 48 yellow balloons. She wants to make balloon bunches using the same number of each colour in every bunch, with no balloons left over.

(a) What is the greatest number of bunches she can make?

(b) How many red and yellow balloons will be in each bunch?

Given,

Red balloons = 36, Yellow balloons = 48.

The greatest number of equal bunches with no balloons left over is the HCF of 36 and 48.

Prime factorisation of 36 and 48:

$\begin{array}{l|r} 2 & 36 \ \hline 2 & 18 \ \hline 3 & 9 \ \hline 3 & 3 \ \hline & 1 \end{array} \quad \text{ and } \quad \begin{array}{l|r} 2 & 48 \ \hline 2 & 24 \ \hline 2 & 12 \ \hline 2 & 6 \ \hline 3 & 3 \ \hline & 1 \end{array}$

⇒ 36 = 2² × 3²

⇒ 48 = 2⁴ × 3

⇒ HCF = 2² × 3 = 4 × 3 = 12

(a) The greatest number of bunches she can make = 12.

(b) Number of red balloons in each bunch = $\dfrac{36}{12}$ = 3

Number of yellow balloons in each bunch = $\dfrac{48}{12}$ = 4

Hence, each bunch will have 3 red and 4 yellow balloons.