Liwanag sold 37 tickets to Manila Zoo. Adult tickets cost Php 3.50 and child tickets cost Php 1.25. She collected 73.25 from the sales of the tickets. How many of each kind were sold?
12 adult and 25 child.
no idea how to do the math, i just guessed and checked until i got the right answer.
X adult tickets: $3.50 ea.
Y child tickets: $1.25 ea.
Eq1: x + y = 37.
Eq2: 3.5x + 1.25y = $73.25.
Multiply Eq1 by -3.5 and add the Eqs.
To solve this problem, we can set up a system of equations. Let's assume that Liwanag sold x adult tickets and y child tickets.
From the problem, we know that Liwanag sold a total of 37 tickets. So we can write our first equation:
x + y = 37
We also know that the total amount collected from the sales of the tickets is Php 73.25. The cost of an adult ticket is Php 3.50, so the total amount collected from the sale of adult tickets is 3.50x. Similarly, the cost of a child ticket is Php 1.25, so the total amount collected from the sale of child tickets is 1.25y. Therefore, our second equation is:
3.50x + 1.25y = 73.25
Now we have a system of equations:
x + y = 37 (Equation 1)
3.50x + 1.25y = 73.25 (Equation 2)
We can solve this system of equations by substitution or elimination. Let's use the elimination method.
First, let's multiply Equation 1 by 1.25 to make the coefficients of y the same in both equations:
1.25 * (x + y) = 1.25 * 37
1.25x + 1.25y = 46.25 (Equation 3)
Now we can subtract Equation 3 from Equation 2:
(3.50x + 1.25y) - (1.25x + 1.25y) = 73.25 - 46.25
3.50x - 1.25x = 27
2.25x = 27
x = 27 / 2.25
x = 12
Now that we have the value of x, we can substitute it back into Equation 1 to find the value of y:
12 + y = 37
y = 37 - 12
y = 25
So, Liwanag sold 12 adult tickets and 25 child tickets.