Formulas with more than one letter-number

Ketaki makes coconut-jaggery laddus. A coconut costs ₹35 and 1 kg of jaggery ₹60. For 10 coconuts and 5 kg of jaggery: 10 × 35 = ₹350, 5 × 60 = ₹300, total ₹650. Try 8 coconuts and 9 kg yourself.

Here two things change, so we need two letter-numbers: c coconuts and j kg of jaggery. Total cost: c × 35 + j × 60. Its terms are c × 35 and j × 60.

For 7 coconuts and 4 kg: 7 × 35 + 4 × 60 = 245 + 240 = ₹485. Different values of c and j give different totals: that is what the expression is for.

More stories to write as expressions:

• Munirathna has a 20 m pipe and joins another piece k m long: total length 20 + k.
• Venkatalakshmi's flour mill takes 10 seconds to start, then 8 seconds per kg of grain: for y kg it takes 10 + 8 × y seconds. (Not (10 + 8) × y: the 10 seconds is paid only once.)

You already know some such rules. A square with side q has perimeter 4 × q; for q = 7 cm that is 28 cm. Rules written with letter-numbers are often called formulas.

Try writing formulas for the perimeter of: an equilateral triangle (3 × side), a regular pentagon (5 × side), a regular hexagon (6 × side). (Regular means all sides and all angles are equal.)