Question

The admission fee at an amusement park is $2.00 for children and $7.00 for adults. On a certain day, 296 people entered the park, and the admission fees collected totaled 1092 dollars. How many children and how many adults were admitted?

number of children equals:
number of adults equals:

Answer 1

This is a system of linear equations problem. Let x be the number of children and y be the number of adults. Then we have:

{x+y=2962x+7y=1092​

We can solve this system by using substitution, elimination, or matrix methods. One possible way is to multiply the first equation by -2 and add it to the second equation to eliminate x:

−2x−2y2x+7y5y​=−592=1092=500​​

Then we can divide both sides by 5 to get y:

y=5500​=100

Now we can plug y into the first equation and solve for x:

x+100=296x=296−100=196

Therefore, the number of children is 196 and the number of adults is 100.