Question

jen is shopping online for a new pair of hiking boots. at checkout, she will use a promotion code on her purchase. the table shows the relationship between the original price of the boots, p, and the price after jen uses the promotion code, c.

original price (p) | $50 | $65 | $80 | $95
price after promotion code (c) | $30 | $45 | $60 | $75

which of the variables is independent and which is dependent?

c is the independent variable, and p is the dependent variable.
p is the independent variable, and c is the dependent variable.

complete the sentence.

the dependent variable is always 20 more than, 20 less than, 20 times, 1/20 of the independent variable.

Explanation:

Part 1: Identifying Independent and Dependent Variables

To determine independent and dependent variables, we analyze the relationship: the price after promotion (\(c\)) depends on the original price (\(p\)) because the promotion is applied to the original price. So \(p\) is independent (it doesn't depend on \(c\)), and \(c\) is dependent (it depends on \(p\)).

We check the relationship between \(p\) and \(c\) using the table:

• For \(p = 50\), \(c = 30\) (\(50 - 20 = 30\))
• For \(p = 65\), \(c = 45\) (\(65 - 20 = 45\))
• For \(p = 80\), \(c = 60\) (\(80 - 20 = 60\))
• For \(p = 95\), \(c = 75\) (\(95 - 20 = 75\))

Thus, \(c = p - 20\), meaning the dependent variable (\(c\)) is always 20 less than the independent variable (\(p\)).

Answer:

\(p\) is the independent variable, and \(c\) is the dependent variable.

Part 2: Completing the Sentence