Two-step equation word problems
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The perimeter of Tina's rectangular garden is 60 feet. If the length of the garden is twice the width, what are the dimensions of the garden? So let's draw this garden here, Tina's garden. So it's a rectangle. They tell us that it's a rectangular garden. So it looks something like this. And let's say that this is the width. So if this is the width, then this is also going to be the width. And this is the length up here. And they tell us that the length of the garden is twice the width. So if this is w, then the length is going to be 2w. It's going to be twice the width. This is also going to be 2w over here. Now, what's the perimeter of this garden? Well, it's going to be w plus w plus 2w plus 2w. Let me write this down. The perimeter of this garden is going to be equal to w plus 2w plus w plus 2w, which is equal to what? This is w plus 2w is 3w, 4w, 6w. So this is equal to 6w. That's the perimeter in terms of the width. But they also tell us that the actual numerical value of the perimeter is 60 feet. It is 60 feet. So this perimeter 6w must be equal to 60 if we assume that we're dealing with feet. So we just have the equation 6w is equal to 60. We can divide both sides of this equation by 6 so that we have just a w on the left-hand side. 6w divided by 6 is just w. And then 60 divided by 6 is 10. So we have w is equal to 10. So the width of the garden is 10. So this distance over here is 10. And then what is the length of the garden? Well, it's 2 times the width. So this is equal to 20. The length is equal to 20. And so we're done. This is a 20 by 10 garden.