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Video: Solving One-Step Multiplication Linear Equations in a Real-World Context

Tim Burnham

A Quetzal bird’s tail can be twice as long as its body. The equation 2𝑏 = 14 describes the length of a certain Quetzal bird’s tail in inches. If 𝑏 is the length of the Quetzal bird’s body, determine the value of 𝑏 and the total length of the bird.

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Video Transcript

A Quetzal bird’s tail can be twice as long as it’s body. The equation two 𝑏 equals fourteen describes the length of a certain Quetzal bird’s tail in inches. If 𝑏 is the length of the Quetzal bird’s body, determine the value of 𝑏 and the total length of the bird.

So we’ve got the Quetzal bird, which can have a very long tail. Now the equation two 𝑏 equals fourteen describing the length of the bird’s tail in inches, that tells us that two 𝑏 is the length of the tail. So the length of the tail is fourteen inches, and we’re also told that 𝑏 is the length of the bird’s body.

So let’s just write those facts down, and that can help you to understand what you’ve got to do in the question. So the length of the tail is two 𝑏 equals fourteen, and the length of the body is equal to 𝑏. Now we’ve got to find out the value of 𝑏 and then go on to calculate the total length of the bird.

Well if two 𝑏 equals fourteen, to work out the value of one 𝑏, I just need to divide both sides of that equation by two. And on the left-hand side, a half of two 𝑏 is just 𝑏 and a half of fourteen is seven. So we know that 𝑏 is equal to seven. Well that’s the first part of the question answered. And now the total length of the bird will be the length of the tail plus the length of the body, so that’s going to be two 𝑏 plus 𝑏.

Now I’ve no idea what a real Quetzal bird looks like, but let’s assume it looks like this. The length of its body would be 𝑏. And with a tail of two 𝑏, the total length of the bird would be 𝑏 plus two 𝑏.

And remember 𝑏 is seven and two 𝑏 is fourteen, so the overall length of bird including its tail is seven plus fourteen, which is twenty-one. And not forgetting our units there, we know that 𝑏 is equal to seven, and the total length of the bird is twenty-one inches.