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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? [A] 64 passengers were on a bus. When 81 passengers joined them, the total was 𝑥. [B] 64 passengers were on a bus. When 𝑥 passengers got on the bus, the total number of passengers was 81. [C] 𝑥 passengers were on a bus. When 81 passengers got off the bus, there were 64 passengers left. [D] 𝑥 passengers were on a bus. When 64 passengers got off the bus, there were 81 passengers left.

03:57

Video Transcript

Which of the following could be described by sixty-four plus 𝑥 equals eighty-one? Let’s go through and look at some keywords that will help us come to a conclusion. A, B, C, and D all speak about passengers that are on a bus. Our equation adds sixty-four in 𝑥 to result in a final answer of eighty-one, that means we need to have eighty-one passengers on our bus at the end. Since we’re adding sixty-four in 𝑥 that means passengers got on the bus. Because we are adding 𝑥. We are adding people to our amount of sixty-four, which is why it results in a bigger number which is eighty-one. So let’s go through our options: A, B, C, and D and eliminate some of these.

The first sentence for every option of A, B, C, and D are all Okay. A says there are sixty-four passengers on the bus, B says the exact same thing, and C and D says that there’s 𝑥 passengers were on the bus. Now since addition is commutative, meaning sixty-four plus 𝑥, and 𝑥 plus sixty-four mean the exact same thing. It wouldn’t matter if we started with sixty-four or if we started with 𝑥. Now preferably, since sixty-four is written first, we should use the sixty-four first, but let’s keep reading. It’s these second sentences that are crucial. Option A: the second sentence says when eighty-one passengers join them, the total was 𝑥. This is wrong. Eighty-one passengers did not get on the bus. Eighty-one should be the total.

Option B, our second sentence says when 𝑥 passengers got on the bus — that’s good because we added to our sixty-four, so they joined the passengers — the total number of passengers was eighty-one. This seems to work great. Let’s check our other options to be sure. Option C, 𝑥 passengers were on a bus. When eighty-one passengers got off the bus, there were sixty-four passengers left. This is incorrect. Eighty-one passengers did not get off the bus. In our equation, we did not subtract eighty-one passengers nor was our answer sixty-four. Then option D says 𝑥 passengers were on a bus. When sixty-four passengers got off the bus, there were eighty-one passengers left. The fact that there’s eighty-one passengers left meaning eighty-one total at the end, that’s good. However, it says sixty-four passengers got off the bus. We did not subtract sixty-four in order to get an answer of eighty-one. Therefore, D is incorrect.

Therefore our final answer is B. Let’s go through this equation and through our answer and make sure it works. Sixty-four passengers were on a bus when 𝑥 passengers got on the bus. So 𝑥 number people join them, so we add to the sixty-four. The total, which means we should write out equal sign, the total number of passengers was eighty-one, which is sixty-four plus 𝑥 equals eighty-one. So B is our final answer.