Question

The admission fee at an amusement park is $2.75 for children and $5.20 for adults. On a certain day, 322 people entered the park, and the admission fees collected totaled 1253 dollars. How many children and how many adults were admitted?

Answer 1

Solving a system of equations using the elimination method, we find that 172 children and 150 adults were admitted to the amusement park.

Step-by-step explanation:

The question involves solving a system of linear equations to determine how many children and adults were admitted to an amusement park based on the total number of people and the total admission fees collected. Let us define two variables: let c be the number of children and a be the number of adults. We have two equations based on the given information:

• Equation for the number of people: c + a = 322
• Equation for the total cost: 2.75c + 5.20a = 1253

To solve this system of equations, we can use either the substitution method or the elimination method. We'll use the elimination method here:

1. Multiply the first equation by 2.75 to make the coefficients of c in both equations the same. This gives us: 2.75c + 2.75a = 885.5
2. Subtract the modified first equation from the second equation: (2.75c + 5.20a) - (2.75c + 2.75a) = 1253 - 885.5, which simplifies to 2.45a = 367.5
3. Now solve for a: a = 367.5 / 2.45, which gives us a = 150
4. Substitute the value of a back into the first equation: c + 150 = 322, which gives us c = 322 - 150
5. Finally, c = 172

Hence, 172 children and 150 adults were admitted.