Writing Equations from Situations

Say what the letter stands for before writing anything. "Let m be the number of months."

Two ways of saying the same total

When two plans cost the same, each side of the equation is one plan’s cost.

An example

Plan A is 20 + 5m, plan B is 30 + 4m. Equal costs means 20 + 5m = 30 + 4m.

Answer the question asked

Solving gives m = 10. The question may want the cost, which is another step.

Define the variable in words

Write "let x be the number of hours" before anything else. In a problem with several quantities, an undefined letter is a guarantee of confusion later, and the definition takes one line.

Find the two things that are equal

An equation records an equality. "Two plans cost the same" gives one; "the total is £50" gives another. Locating the sentence that asserts equality tells you where the equals sign belongs.

Fixed amounts and rates

Most Grade 8 situations have a fixed part and a rate: a joining fee plus a monthly charge. That structure is exactly y = mx + b, so recognising it gives you the equation almost immediately.

Interpret the solution

A solution of x = 6 becomes "the two plans cost the same after 6 months". Stating the answer in context forces you to check it is sensible — a negative or fractional number of months would signal a modelling error.