Video: Writing and Solving One-Step Linear Multiplication Equations

It takes James 5 times longer than it takes Olivia to get to work. If James’s journey is 70 minutes, write an equation for the time (𝑥) it takes Olivia to get to work. Then solve the equation.

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Video Transcript

It takes James five times longer than it takes Olivia to get to work. If James’s journey is 70 minutes, write an equation for the time 𝑥 it takes Olivia to get to work. Then solve the equation.

In this question, we need to write an equation and then solve it. We’re told in the question that it takes Olivia 𝑥-minutes to get to work. It takes James five times longer. Five multiplied by 𝑥 is equal to five 𝑥. Therefore, it takes James five 𝑥 minutes to get to work. We’re also told that James’s journey time is actually 70 minutes. This means that we have a linear equation five 𝑥 is equal to 70.

As we have now written the equation, we can move on to the second part of the question, which is to solve it. We know that James’s journey time is 70 minutes. And we need to solve the equation five 𝑥 equals 70 to work out Olivia’s journey time. This is a one-step equation as we only need to carry out one calculation to solve it. Remember, we need to perform the same calculation or operation to both sides of the equation. In this case, we will divide by five. Dividing by five is the inverse or reciprocal of multiplying by five.

Five 𝑥 divided by five is equal to 𝑥 as the fives cancel. 70 divided by five is equal to 14. If we couldn’t work out this calculation mentally, we could use the short division bus stop method. Seven divided by five is equal to one remainder two. And 20 divided by five is equal to four. Therefore, 70 divided by five equals 14. The solution of the equation five 𝑥 equals 70 is 𝑥 equals 14. We can therefore conclude that it takes Olivia 14 minutes to get to work.

We can check this answer by considering James’s time and multiplying five by 14. As 70 divided by five was 14, we know that five multiplied by 14 must be equal to 70. Multiplication and division are the opposite or reciprocal of one another. James’s journey time was 70 minutes, which is five times longer than Olivia’s of 14 minutes.

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