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Video: Relating a Real-Life Situation to a One-Variable Equation

Bethani Gasparine

Which of the following could be described by 64 + 𝑥 = 81?

03:08

Video Transcript

Which of the following could be described by 64 plus 𝑥 equals 81?

Each of our options A, B, C, and D talk about passengers on a bus. So looking at our equation of 64 plus 𝑥 equals 81 means we have 64 passengers on a bus. We’re adding 𝑥, so adding a certain number onto that bus, so people are joining on the bus. And there’s a total of 81 on the bus at the end.

Let’s go through each option, paying close attention to the important numbers and words.

Option A says there were 64 passengers on a bus. That’s great. When 81 passengers joined them, the total was 𝑥. Here’s where our issue comes. 81 passengers did not join the 64. We did not have 64 plus 81, and our total was not 𝑥, so A is incorrect.

Option B says 64 passengers were on the bus. When 𝑥 passengers got on the bus, the total number of passengers was 81. This seems to work great. Let’s go ahead and check options C and D just to be sure.

Option C says 𝑥 passengers were on a bus. Technically, we would prefer 64 to be written first. However, 64 plus 𝑥 is commutative, so 64 plus 𝑥 is actually equal to 𝑥 plus 64. So if they would like to write 𝑥 first, it would be okay. However, we would prefer 64 be written first.

Moving on to the second sentence, it says when 81 passengers got off the bus, there were 64 passengers left. Here’s where option C is no longer a good answer. If 81 passengers got off the bus, they would be subtracting 81, which we do not do, and 64 was not our final answer.

Option D says 𝑥 passengers were on a bus. When 64 passengers got off the bus, there were 81 passengers left. It’s good that 81 was the final answer. However, 64 passengers got off the bus means we will be subtracting 64. This is why D is incorrect.

Looking at option B once again, it says 64 passengers were on a bus. When 𝑥 passengers got on the bus, which would mean we are adding to that 64 amount, the total number of passengers was 81.

Total means we should have our equal sign, and the total was 81. Therefore, option B is our final answer.