# Video: Solving Word Problems Involving the Distributive Property

Amelia has not been using the elevator at her building for eight weeks. She climbed up and down 354 steps every day for the duration of that period. Use the distributive property to determine the number of steps she climbed during that period.

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### Video Transcript

Amelia has not been using the elevator at her building for eight weeks. She climbed up and down 354 steps every day for the duration of that period. Use the distributive property to determine the number of steps she climbed during that period.

Before we can go on and solve this problem, we need to actually understand what the distributive property is. Well the distributive property is that if we have a number 𝑥 and we multiply it by 𝑎 plus 𝑏, then this is equal to 𝑥 multiplied by 𝑎 plus 𝑥 multiplied by 𝑏. And to give an example of this, if I had two multiplied by three plus four, this will be equal to 14 because it’d be two multiplied by, and then three plus four which is seven, so two multiplied by seven, which is 14.

And if I had two multiplied by three plus two multiplied by four, this would be equal to six plus eight, which would also be equal to 14, so therefore demonstrating the distributive property. Okay, great! Now we know what the distributive property is, let’s go on and solve the problem. Well the first thing I want to do is actually find out the number of days, because it says that Amelia has not been using the elevator at her building for eight weeks. And she climbed up and down the steps every day.

So therefore the number of days is gonna be equal to eight, because that is the number of weeks, multiplied by seven, because that is the number of days in a week. So therefore, it’s gonna be 56 days. So we’re looking at a 56-day time period. Okay, great! So now let’s go on and solve the rest of the problem. Okay, now we want to actually calculate the total number of steps.

And the key thing to note here is that it says that she climbed up and down 354 steps every day. So we need to find the total number of steps up and the total number of steps down. So this is gonna be equal to 354, which is the number of steps up, multiplied by 56, which is the number of days, plus 354, again this time the steps down, multiplied by 56, the total number of days.

So therefore using the distributive property, we can say this is the same as 56 multiplied by, and then 354 plus 354 because the number of steps up plus the number of steps down. So this is gonna be equal to 56 multiplied by 708. So therefore, we can say that the total number of steps that she climbed during the eight weeks is equal to 39648.