Representing Relationships Flashcards

A pizza restaurant charges a flat fee of $3 for delivery and $11 for each pizza ordered. Which equation can be used to find the total cost (C) for any number of pizzas (p)?

Answer: C = 11p + 3

The total cost (C) is the sum of the cost of the pizzas and the delivery fee. The cost of the pizzas is $11 times the number of pizzas (p), which is 11p. The delivery fee is a constant $3. Therefore, the correct equation is C = 11p + 3.

The table below shows the relationship between the number of hours a student spends studying (h) and the score they receive on a test (S). Which rule describes this relationship? | Hours (h) | Score (S) | |---|---| | 0 | 65 | | 1 | 72 | | 2 | 79 | | 3 | 86 |

Answer: S = 7h + 65

The score (S) starts at 65 when the hours (h) are 0. For each additional hour of studying, the score increases by 7. This can be represented by the equation S = 7h + 65. Let's test it: for h=2, S = 7(2) + 65 = 14 + 65 = 79, which matches the table.

Which of the following verbal statements correctly represents the algebraic expression 2(n - 5)?

Answer: Twice the difference of a number and five.

The expression (n - 5) represents 'the difference of a number and five'. The number 2 outside the parentheses indicates that this entire difference is multiplied by two, or 'twice' the difference.

A taxi company charges $2.50 for the first mile and $0.75 for each additional mile. If 'm' represents the total number of miles traveled, which expression represents the total cost for a ride that is more than one mile?

Answer: 2.50 + 0.75(m - 1)

The cost includes a flat fee of $2.50 for the first mile. The variable 'm' is the total miles. Since the first mile is already paid for by the $2.50 fee, the additional charge of $0.75 applies only to the remaining miles, which is represented by (m - 1). Thus, the total cost is 2.50 + 0.75(m - 1).

The perimeter of a rectangle is found using the formula P = 2L + 2W, where L is the length and W is the width. If the length of a rectangle is 4 units more than its width (W), which equation represents the perimeter in terms of only its width?

Answer: P = 2(W + 4) + 2W

The problem states that L = W + 4. To write the perimeter formula in terms of only W, we substitute (W + 4) for L in the original formula: P = 2(W + 4) + 2W.

A pattern of figures is shown below. If 'n' represents the figure number, which expression can be used to find the number of squares in any figure? Figure 1: 3 squares Figure 2: 5 squares Figure 3: 7 squares

Answer: 2n + 1

The number of squares increases by 2 for each new figure. This suggests a relationship involving 2n. Let's test the expression 2n + 1. For Figure 1 (n=1), 2(1) + 1 = 3. For Figure 2 (n=2), 2(2) + 1 = 5. For Figure 3 (n=3), 2(3) + 1 = 7. The expression correctly describes the pattern.