Working Backward
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 51 of 58.
Sometimes the story gives the output and asks for the input. A student paid the music school 135 dollars in all. How many lessons did they take? That asks for the n with C(n) = 135.
Use the rule to turn it into an equation: 25 + 10n = 135. Undo the fixed part first, since it was added last when the cost was built: subtract 25 to get 10n = 110. Then undo the multiplication: divide by 10, so n = 11. Eleven lessons.
Check it forwards: 25 plus 10 times 11 is 135. And check it against the story: the answer counts lessons, so it must be a whole number. If you ever get 11.5, either the working or the bill is wrong.
Challenge
The gym's cost for n visits is C(n) = 15 + 4n dollars. A climber paid 87 dollars in all. Solve C(n) = 87 to find how many visits they made.
Try it yourself
Solve for n
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Functions & Transformations
4Combining Functions
Adding FunctionsSubtracting FunctionsMultiplying FunctionsAt a Single NumberRecap: Combining10Functions in Stories
Writing the RuleUsing the RuleWorking BackwardUndoing a ConversionRecap: Stories2Expressions as Inputs
A Letter as InputA Sum as InputShifting the InputSolving f(x) = kRecap: Inputs as Expressions5Composition
One Inside AnotherOrder MattersA Function of ItselfComposing RulesBreaking ApartRecap: Composition8Stretching and Flipping
Taller and FlatterFlipping OverFlip, Then ShiftReading the RuleRecap: Stretch and Flip