Question

d. tickets to the zoo cost $25 for adults and $10 for children. the total ticket sales one day were $47,750. the number of children, c, who visited the zoo was 270 more than 6 times the number of adults, a, who visited. write and solve a system of equations to find the total number of visitors to the zoo that day.

a +

c = $47,750

a +

a =

c =

total visitors

Explanation:

Step1: Define variables and equations

Let \( a \) be the number of adult visitors and \( c \) be the number of children visitors.
From the problem, we have two equations:

1. The number of children is 270 more than 6 times the number of adults: \( c = 6a + 270 \)
2. The total ticket sales: \( 25a + 10c = 47750 \)

Step2: Substitute \( c \) into the sales equation

Substitute \( c = 6a + 270 \) into \( 25a + 10c = 47750 \):
\( 25a + 10(6a + 270) = 47750 \)

Step3: Simplify and solve for \( a \)

Expand the equation:
\( 25a + 60a + 2700 = 47750 \)
Combine like terms:
\( 85a + 2700 = 47750 \)
Subtract 2700 from both sides:
\( 85a = 47750 - 2700 = 45050 \)
Divide by 85:
\( a = \frac{45050}{85} = 530 \)

Step4: Find \( c \) using \( c = 6a + 270 \)

Substitute \( a = 530 \):
\( c = 6(530) + 270 = 3180 + 270 = 3450 \)

Step5: Find total visitors

Total visitors = \( a + c = 530 + 3450 = 3980 \)

Answer:

• \( a = 530 \)
• \( c = 3450 \)
• Total visitors = \( 3980 \)