Math Lesson 9.2.3 - Solving Problems that Involve More than Two Steps

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Welcome to our Math lesson on Solving Problems that Involve More than Two Steps, this is the third 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 Problems that Involve More than Two Steps by Using First-Order Equations with One Variable

There are a number of situations where the problem requires the application of more than two steps, although the equation used is still a first - order equation with one variable. For example, if there are two friends, Andy and Bill who have posted a total 53 videos on social media, where Andy has posted five videos more than double of Bill, and the problem requires the number of videos posted by each friend, this problem involves more than two steps. Thus, first, we have to calculate the number of videos posted by the two friends taken together if Andy would have posted exactly double the number of Bill's videos. For this, we have to subtract 5 from 53, i.e. 53 - 5 = 48.

The next step includes the use of proportion approach to find the number of videos posted by Bill. Thus, since A + B = 48 and A = 2B, we have 2B + B = 48, so 3B = 48 and therefore, B = 48/3/ = 16.

The next step involves multiplying the number of Bill's videos by 2 to calculate the number of videos posted by Andy if he had posted exactly twice the number of Bill's videos. Thus, A = 2B = 2 × 26 = 32.

However, since Andy has in fact posted five more videos than double of Bill's, we have a last step still to follow. Thus, in fact Andy has posted A = 32 + 5 = 37 videos in social media.

Obviously, this is a long and time - consuming procedure. We can instead create an equation from the clues and solve everything in a much shorter way. We can write

and since A = 2B + 5, we can substitute it in the above equation to obtain the number of videos posted by Bill. Thus,

In this way, the number of videos posted by Andy therefore is

Hence, the result is the same as that obtained by means of the previous method, as expected.

Example 3

Stacy's age is 12 years more than triple the age of her daughter Cindy, while Mary, the mother of Stacy is 22 years older than Stacy. Calculate Mary's age if Cindy is 9 years old.

Solution 4

1. 1st step: We calculate what is triple the Cindy's age. This number is 3 · C = 3 · 9 = 27.
   2nd step: Now, we calculate Stacy's age. Thus, S = 27 + 12 = 39.
   3rd step. Finally, we calculate Mary's age. We have M = S + 20 = 39 + 20 = 59.
   
2. We can express this situation through a single equation. Thus, we can write
   M = S + 20
   where S = 3C + 12. Thus, substituting this last expression in the original equation yields
   M = (3C + 12) + 20
   = 3C + 12 + 20
   = 3C + 32
   = 3 · 9 + 32
   = 27 + 32
   = 59

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

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