A ratio of 3:1 means that there are 3 home fans for every one visiting fan. So, of every 4 fans, 3 are home fans and \( \frac{3}{4} \) of every fan in the stadium is a home fan:

49,000 fans x \( \frac{3}{4} \) = \( \frac{147000}{4} \) = 36,750 fans.

The area of a rectangle is width (w) x height (h). In this problem we know that the rectangle is twice as long as it is wide so h = 2w. The perimeter of a rectangle is 2w + 2h and we know that the perimeter of this rectangle is 54 meters so the equation becomes: 2w + 2h = 54.

Putting these two equations together and solving for width (w):

2w + 2h = 54
w + h = \( \frac{54}{2} \)
w + h = 27
w = 27 - h

From the question we know that h = 2w so substituting 2w for h gives us:

w = 27 - 2w
3w = 27
w = \( \frac{27}{3} \)
w = 9

Since h = 2w that makes h = (2 x 9) = 18 and the area = h x w = 9 x 18 = 162 m²

The greatest common factor (GCF) is the greatest factor that divides two integers.

Betty scored 77% on the test meaning she earned 77% of the possible points on the test. There were 210 possible points on the test so she earned 210 x 0.77 = 162 points. Each question is worth 3 points so she got \( \frac{162}{3} \) = 54 questions right.

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