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A carnival charges $3 for kids and $10 for adults. On Saturday, there were 500 visitors, and the total amount taken at the gate was $3,600. The equation representing the number of visitors is k + a = 500, where k represents the number kids and a represents the number of adults. The equation representing the amount of money collected is 3k + 10a = 3,600. How many kids and adults visited the carnival?

The number of adults, a, is 300, and the number of kids, k, is 200.

Step-by-step explanation:

k + a = 500 (1)

3k + 10a = 3,600 (2)

Multiply both sides of equation (1) by - 3.

(k + a) • - 3 = 500 • - 3

-3k - 3a = - 1,500

Now, add this equation to equation (2).

3k + 10a = 3,600

+ - 3k - 3a = - 1,500

7a = 2,100

a = 300

Substitute the value of a into equation (1).

k + a = 500

k + 300 = 500

k = 500 - 300

k = 200

In the system of equations, a represents the number of adults and k represents the number of kids who visited the carnival. The number of adults, a, is 300, and the number of kids, k, is 200.