Percent Equations
Part of the Fundamentals section of Coddy's Algebra journey. Lesson 44 of 64.
Take the sentence "20% of a number is 15". Percent means per hundred, so 20% is 20/100, which is 1/5 or 0.2. The word "of" means multiply. So the sentence becomes the equation:
20% × x = 15
Write the percent as a fraction over 100, and the equation has a fraction coefficient: 1/5 x = 15. Multiply both sides by 5 to get x = 75. Check the answer: a fifth of 75 is 15.
Every "what number" percent question has this shape. "12 is 30% of what?" becomes 30% × x = 12. "What is 15% of 80?" becomes x = 15% × 80, and that needs no solving, only arithmetic. Write the sentence as an equation, then solve it the way you already know.
Challenge
MediumSolve the equation 25% × x = 12 for x.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Fundamentals
1What an Equation Is
The EquationFinding the UnknownThe Same to Both SidesSolved Means AloneRecap: First Equations4Two-Step Equations
Two Layers to UndoSubtract, Then DivideAdd, Then DivideA Division InsideNegatives in Two StepsRecap: Two-Step Equations2One-Step Equations
Undoing AdditionUndoing SubtractionUndoing MultiplicationUndoing DivisionInverse OperationsRecap: One-Step Equations5Tidying First
Like TermsTerms and Numbers MixedThe Distributive PropertyDistributing a SubtractionTidy, Then SolveRecap: Tidying First8Decimals and Percent
Decimal CoefficientsTwo-Step with DecimalsAdding a PercentPercent EquationsRecap: Decimals