Question

the admission fee at an amusement park is $2.25 for children and $6.20 for adults. On a certain day, 220 people entered the park and the admission fees collected totaled $890 dollars. how many children and how many adults were admitted?

Answer 1

In order to do this you need a system of equations.  One equation is going to be about the numbers of people, the other is going to be about the money: what it costs for each type of person and the total amount of money earned.  Money and numbers of people are 2 different things so they have to be in 2 different equations.  We know that there were children and adults that went to the park and that the total NUMBER of people is 220.  That means that adults plus children equal 220 people total.  Or, in equation form, a + c = 220.  Now the money part.  Each child costs 2.25, so the cost of a child is 2.25c; each adult costs 6.20, so the cost of an adult is 6.20a.  The total amount of money earned was 890.  That equation is 2.25c + 6.20a = 890.  Solve the first equation for a:  a = 220 - c.  Now sub in that value for a in the money equation, like this: 2.25c + 6.20(220-c) = 890.  Solve this for c.  2.25c+1364-6.2c = 890.  Combine like terms to get -3.95c = -474.  Divide both sides by 3.95 to get that c = 120.  There were 120 children out of the 220 people that attended.  That means that there were 220-120 adults, or 100 adults.  There you go!