A small fair charges an admission fee for children and adults. The cost for admission is $3 per adult and $2 per child. On a certain day, total admission fees were $900, and 350 people attended the fair. How many children attended the fair that day?

150 children attended the fair that day

Step-by-step explanation:

Let n represents the number of children attended.

Since there were 350 people attended, the number of adults is 350-n

Since the cost of admission is $3 per adult, the admission fee gained by adults is:

→ 3(350-n)  (1)

Since the cost of admission is $2 per child, the admission fee gained by children is:

→ 2n  (2)

Since the total admission fees were $900, the total of 1 and 2 must be equal to 900

→ 3(350-n) + 2n = 900

→ 1050 - 3n + 2n = 900

→ n = 150

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus