Forming and Solving Equations

Algebra and Sequences

An equation needs two expressions for the same quantity, set equal
Read the sentence for the fact that links them: a total, a perimeter, an angle sum, or two costs being equal
Check the expression before solving by substituting a trial value

Worked example

Consecutive integers

Three consecutive integers have a sum of 84. Find the integers.

Solution:

Name the unknown first, and choose the one the others can be written from
Let the smallest integer be n
Consecutive means each is one more than the last, so the other two are n + 1 and n + 2
Writing all three in terms of a single letter is what makes this solvable with one equation
Their sum is 84, which gives n + (n + 1) + (n + 2) = 84
Collect the three n terms and the two numbers: 3n + 3 = 84
Subtract 3 from both sides: 3n = 81
Divide by 3: n = 27
The integers are 27, 28 and 29
Answer the question rather than stopping at n = 27, and check: 27 + 28 + 29 = 84