A roll of ribbon is cut into three pieces in the ratio of 7 : 2 : 3. The shortest piece is 42 cm. What is the length of the longest piece of ribbon?

1. Identify the number of units for the shortest piece and find the value of 1 unit

The ratio is $7 : 2 : 3$. The shortest piece corresponds to $2$ units.
$2 \text{ units} = 42 \text{ cm}$
$1 \text{ unit} = 42 \div 2 = 21 \text{ cm}$

2. Identify the number of units for the longest piece and calculate its length

The longest piece corresponds to $7$ units.
Length of longest piece $= 7 \times 21 = 147 \text{ cm}$