Math Lesson 9.2.2 - Two-Steps Problems Using First-Order Equations

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Welcome to our Math lesson on Two-Steps Problems Using First-Order Equations, this is the second 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 Two-Steps Problems Using First-Order Equations with One Variable

Let's consider again the above problem with a small change. Now, the babysitter is given to be five times the sum of twins' age. The problem requires finding the babysitter's age. Therefore, we have to write her age by x. However, since the babysitter's age is five times the sum of twins' age, first we must calculate this sum and then multiply it by 5. Therefore, this problem includes two steps, although there is still to use a first - order equation (2 · 3 · 5 = x). Solving this equation gives x = 30, i.e. the babysitter is 30 years old (as expected).

Example 2

Anna and Marc have in total $86. Anna has $4 more than Marc. How much money does Anna have?

Solution 2

1. 1st step: We must first calculate the sum if Marc had the same amount as Anna. For this, we have to subtract 4 from the original sum. We have $86 - $4 = $82.
   2nd step: Now, we must divide the last number by 2 to find how much money does Anna have. Thus, A = $82 ÷ 2 = $41.
2. We can express the amount possessed by Anna by A. In this way, since M = A + 4, we obtain the equation
   A + (A + 4) = 86
   A + A + 4 = 86
   2A + 4 = 86
   2A + 4 - 86 = 86 - 86
   2A - 82 = 0
   We have a = 2 and b = -82 in this first - order equation with one variable. Thus, since in such equations the variable is calculated as x = - b/a, we have (here x = A):
   A = - (-82/2
   = $82/2
   = $41

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