Question

Read the following word problem. Give the system of equations AND the solution: Ms. Rubio needs to know how many students and adults went to an Edison football game. She knows there were a total of 429 people there (all either adults or students) and she made $2,077 in admission tickets. If student tickets cost $3 and adult tickets are $8, how many students were at the game? How many adults?

Answer 1

To solve this problem, set up a system of equations with the number of students as 's' and the number of adults as 'a'. Solve the system using substitution or elimination to find the values of s and a. The solution is 271 students and 158 adults.

Step-by-step explanation:

To solve this problem, we need to set up a system of equations. Let's define the number of students as 's' and the number of adults as 'a'. From the problem, we know that s + a = 429 (equation 1) and 3s + 8a = 2077 (equation 2). To find the solution, we can solve this system of equations using substitution or elimination.

One way to solve this system is by substitution. We can rearrange equation 1 to solve for a: a = 429 - s. Now we substitute this value of a in equation 2: 3s + 8(429 - s) = 2077. Simplifying this equation gives us 3s + 3432 - 8s = 2077. Combining like terms, we get -5s + 3432 = 2077. Then by solving for s, we get s = 271.

Substituting this value of s back into equation 1, we can find the value of a: 271 + a = 429. Solving for a, we get a = 158. Therefore, there were 271 students and 158 adults at the Edison football game.