Admission to an amusement park is $10 for children and $15 for adults. On Saturday 1,300 people enter the park and $17,250 is collected. How many children and adults entered the park?

Simple

suppose number of adults entered park on Saturday be = x

number of children entered park on Saturday be = y

so we get equation

x + y = 1300

x = 1300 - y { equation 1}

now for each children ticket is 10$ and y number of children visited park on Saturday. so children collection on Saturday = 10y

similarly adult collection = 15x

15x+10y=17250

divide all by 5

3x+2y=3450

put x = 1300 - y from equation 1 here

3 (1300-y) + 2y=3450

3900 - 3y + 2y = 3450

3900 - y = 3450

3900-3450 = y

450 = y

so number of children visited park on saturday = 450

number of adult visited park on saturday = 1300 - 450 = 850