Math Lesson 9.2.1 - One-Step Problems Using First-Order Equations

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Welcome to our Math lesson on One-Step Problems Using First-Order Equations, this is the first lesson of our suite of math lessons covering the topic of Word Problems Involving Equations, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Solving One-Step Problems Using First-Order Equations with One Variable

The simplest wordy problems are those that are solved through a single step. In general, such problems are short and they contain one or two clues. The resulting equation, therefore, is a first - order one with one variable, which is the simplest type of equation. Let's clarify this point through an example.

Example 1

Two twins are 3 years old and their babysitter is 36. How many times older than twins is the babysitter?

Solution 1

1. We can solve this wordy problem using the same approach, i.e. in words. Thus, since the babysitter is 36 years old and twins are 3 years old, they are 36 ÷ 3 = 12 times younger than their babysitter, or she is 12 times older than the twins.
2. We can create an equation based on the clues given in the problem. Thus, expressing the age ratio by x, we can write
   3 ∙ x = 36
   3x - 36 = 0
   Since in this first - order equation with one variable the coefficient and constant are a = 3 and b = -36 respectively, we have
   x = - b/a
   = - -36/3
   = 12
   Hence, again the result is that the babysitter is 12 times older than the twins.

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7. Continuing learning equations - read our next math tutorial: Identities

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Equations Calculators by iCalculator™

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