Questions: The number of juniors in a statistics class is 9 less than five times the number of seniors. Let s represent the number of seniors. The number of juniors can be represented by The length of a rectangle is eight feet less than seven times the width. The perimeter is 112 feet.

Solution Steps

1. Question 8: We need to express the number of juniors in terms of the number of seniors, \( s \). According to the problem, the number of juniors is 9 less than five times the number of seniors. Therefore, the expression for the number of juniors is \( 5s - 9 \).

2. Question 9: We need to find the dimensions of a rectangle given the relationship between its length and width, and its perimeter. Let \( w \) be the width of the rectangle. The length is given as eight feet less than seven times the width, so the length can be expressed as \( 7w - 8 \). The perimeter of a rectangle is given by the formula \( 2 \times (\text{length} + \text{width}) \). We can set up the equation \( 2 \times ((7w - 8) + w) = 112 \) and solve for \( w \).

The problem states that the number of juniors is 9 less than five times the number of seniors. Let \( s \) represent the number of seniors. The expression for the number of juniors is:

\[ j = 5s - 9 \]

Given that the number of seniors is 10, we substitute \( s = 10 \) into the equation:

\[ j = 5(10) - 9 = 50 - 9 = 41 \]

The length of the rectangle is eight feet less than seven times the width. Let \( w \) represent the width of the rectangle. The length \( l \) can be expressed as:

\[ l = 7w - 8 \]

The perimeter of the rectangle is given by:

\[ 2(l + w) = 112 \]

Substituting the expression for the length, we have:

\[ 2((7w - 8) + w) = 112 \]

Simplify and solve the equation for \( w \):

\[ 2(8w - 8) = 112 \]

\[ 16w - 16 = 112 \]

\[ 16w = 128 \]

\[ w = 8 \]

Substitute \( w = 8 \) back into the expression for the length:

\[ l = 7(8) - 8 = 56 - 8 = 48 \]

Final Answer