Video: Solving Word Problems That Involves Writing and Solving One-Step Linear Equations

A diver began his ascent to the surface. He ascended 20 meters to his next decompression stop and must ascend another 32 meters to return to the surface. Write and solve a subtraction equation to find the diver’s original depth before he started ascending.

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Video Transcript

A diver began his ascent to the surface. He ascended 20 meters to his next decompression stop and must ascend another 32 meters to return to the surface. Write and solve a subtraction equation to find the diver’s original depth before he started ascending.

The diver started at a depth that we don’t know. We can call this step 𝑥. We do know that the diver ascended 20 meters and still needs to ascend 32 meters before the diver reaches the surface. We want to write and solve a subtraction equation to find 𝑥, the diver’s original depth. If we began with 𝑥, the diver is 𝑥 meters deep and he rises 20 meters. Mathematically, we need to represent that with subtraction because he is not as deep as he was before. Even though he’s going up, he is becoming less deep. It’s his original depth minus the 20 meters he rose. And 𝑥 minus the 20-meter ascent will equal the 32 meters that remain, which means one equation is 𝑥 minus 20 equals 32.

To solve this equation, we add 20 to both sides. 32 plus 20 equals 52. And so, we can say that the diver’s original depth was 52 meters. We’ve written a subtraction problem. And we’ve solved for the missing depth to show that the diver’s original depth before he started ascending was 52 meters.

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