When Mr. J. Raff took his two children to the zoo,their tickets cost $8.75. The next family in line was Mrs. Ella Fant with Grandpa and the five Fant kids. Their tickets cost a total of $19.75. How much does the zoo charge for each adult and for each child?
Raff: a + 2c = 8.75
Fant: 2a + 5c = 19.75
Fant - 2 x Raff:
c = 2.25
so a = 4.25
To find out how much the zoo charges for each adult and each child, we can use algebra.
Let's assume the zoo charges $x for each adult ticket and $y for each child ticket.
According to the given information, Mr. J. Raff (1 adult) and his two children's (2 child) tickets cost $8.75. So we can write the equation:
1x + 2y = 8.75 --(Equation 1)
Similarly, when Mrs. Ella Fant, Grandpa, and the five Fant kids (1 adult and 5 children) purchased their tickets for a total of $19.75, we can write another equation:
1x + 5y = 19.75 --(Equation 2)
Now, we have two equations with two variables. To solve for x and y, we can use a method called "substitution" or "elimination".
Let's use the elimination method to solve:
Multiply Equation 1 by 5 and Equation 2 by 2 to eliminate the x variable:
5(1x + 2y) = 5(8.75)
2(1x + 5y) = 2(19.75)
Simplifying, we get:
5x + 10y = 43.75 --(Equation 3)
2x + 10y = 39.50 --(Equation 4)
Now, subtract Equation 4 from Equation 3 to eliminate the y variable:
(5x + 10y) - (2x + 10y) = 43.75 - 39.50
Simplifying further, we get:
3x = 4.25
Divide both sides by 3:
x = 4.25 / 3
x ≈ 1.417
Now, we have the value of x, which represents the cost of each adult ticket. Let's substitute this value into Equation 1 to find the value of y:
1(1.417) + 2y = 8.75
Simplifying further:
1.417 + 2y = 8.75
2y = 8.75 - 1.417
2y ≈ 7.333
y ≈ 7.333 / 2
y ≈ 3.666
Therefore, the zoo charges approximately $1.42 for each adult ticket and $3.67 for each child ticket.