1.
Leland wants to paint a portrait for his parents using a photograph of them that is 5 inches wide by 8 inches high. He wants the portrait to be proportional to the photograph and 42 inches high. Which proportion can Leland use to find w, the width he needs to use to make the portrait proportional?
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height new / height old = 42/8 = width new / width old = w / 5
w = 5 * 42 / 8
To find the proportion to use in this situation, we need to set up a ratio between the height and width of the photograph and the desired height and width of the portrait.
Let's assign variables to the given dimensions:
Width of the photograph = 5 inches (let's call it x)
Height of the photograph = 8 inches (let's call it y)
Desired height of the portrait = 42 inches
Now, let's set up the proportion using the variables:
(height of the photograph)/(width of the photograph) = (desired height of the portrait)/(unknown width of the portrait)
So, we have:
8/x = 42/y
To solve for the unknown width of the portrait (w), we need to cross multiply:
8 * y = 42 * x
Now, we can rearrange the equation to solve for w (width of the portrait):
w = (8 * y) / 42
Simplifying further, we get:
w = (4y) / 21
Therefore, the proportion Leland can use to find w is:
w = (4y) / 21