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