Question

theadmissin fee is $2.00 for children and $5.40 for adults. on a certain day 269 people entered the park and the park collected $1099. how many childrem and adults were admitted

Answer 1

Using a system of equations and the elimination method to solve for the number of children and adults admitted, we find that there were 104 children and 165 adults.

Step-by-step explanation:

The question involves using a system of equations to determine how many children and adults were admitted to the park based on the admission fee and total collected amount. Let's denote the number of children as C and the number of adults as A. We are given two pieces of information which lead to two equations:

1. The number of children plus the number of adults equals 269:
C + A = 269

2. The total amount collected from children's tickets ($2.00 each) and adults' tickets ($5.40 each) is $1099:
2C + 5.40A = 1099

To solve this system of equations, we can use the substitution or elimination method. For simplicity, let's use the elimination method:

1. Multiply the first equation by 2 to line up with the '2C' in the second equation:
   2C + 2A = 538
2. Subtract the first equation from the second equation:
   (2C + 5.40A) - (2C + 2A) = 1099 - 538
   This simplifies to 3.40A = 561, which we can solve for A to find the number of adults.
3. Divide both sides by 3.40 to solve for A:
   A = 561 / 3.40
   A = 165
4. Substitute the value of A back into the first equation to find C:
   C + 165 = 269
   C = 269 - 165
   C = 104

There were 104 children and 165 adults admitted to the park.