Question

the smith family reunion and the jones family reunion both include a visit to a family friendly amusement in florida. the smith family pays $882.00 for passes for 10 adults and 18 children. the jones family pays $951.00 for passes for 11 adults and 19 children. which equation below can be used to solve for the price of the adult and children admissions?
a. $882 + 951 = (10a + 11a) + (18c + 19c)$
b. $882 - 951 = (10a - 11a) + (18c - 19c)$
c. $882 = 10a - 18c; 951 = 11a - 19c$
d. $882 = 10a + 18c; 951 = 11a + 19c$

Explanation:

Step1: Define Variables

Let \( A \) be the adult ticket price and \( C \) be the child ticket price. Smith's cost: \( 10A + 18C = 882 \). Jones's cost: \( 11A + 19C = 951 \).

Step2: Analyze Option A

Option A: \( 882 + 951=(10A + 11A)+(18C + 19C) \). This combines totals, not helpful for solving \( A \) and \( C \).

Step3: Analyze Option B

Option B: \( 882 - 951=(10A - 11A)+(18C - 19C) \). Simplifies to \( -69=-A - C \), not useful.

Step4: Analyze Option C

Option C: \( 882 = 10A - 18C \); \( 951 = 11A - 19C \). Incorrect, Smith's equation should be \( 10A + 18C = 882 \), not subtraction.

Step5: Analyze Option D

Option D: \( 882 = 10A + 18C \); \( 951 = 11A + 19C \). These match the defined equations for Smith (10 adults, 18 children) and Jones (11 adults, 19 children). Subtracting the two equations (e.g., \( 951 - 882=(11A - 10A)+(19C - 18C) \)) gives \( 69 = A + C \), a step toward solving.

Answer:

D. \( 882 = 10A + 18C \); \( 951 = 11A + 19C \)