Algebra Explained

How are word problems expressed as equations?

There seem to be a gazillion word problems out there—just ask anyone taking such tests in grade or high school! The one thing most have in common is that they can be expressed as an equation—many as algebraic equations—in which there are known and unknown quantities. In almost all instances, there are key words that lead the reader to determine not only the numbers and variables, but what operations to use in the equation to determine the answer. The following lists some simple key words and the corresponding operation:

Key Words Operation Examples
sum, total, more than addition The sum of my weight and 10 equals 130 (y + 10 = 130); the groceries at one store were $3.00 while the total for two stores was $4.00 (y + 3 = 4); seven more than the price is $126 (y + 7 = 126)
difference, discrepancy subtraction The difference (or discrepancy) between her age and her sister’s age, who is 30, is 10 (y - 30 = 10)
times, multiplied by multiplication Three times his brother’s age is 6 (3 × y = 6); eight multiplied by her weight is 96 (y × 8 = 96); the product of his weight and 6
is 36 (y × 6 = 36)


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