Question

The admission fee at an amusement park is $3.25 for children and $5.80 for adults. On a certain day, 369 people entered the park, and the admission fees collected totaled 1671 dollars. How many children and how many adults were admitted?

Answer 1

185 adults and 184 children

Explanation:

People entering the park = adults plus children

369 = a+c

Total money = admission fee for kids * number of children + admission fee for adults * number of adults

1671 = 3.25c + 5.80a

We have 2 equations and 2 unknowns

Solve the first equation for a by subtracting c from each side

369-c = a+c-c

369-c =a

Substitute this in to the second equation

1671 = 3.25 c +5.80 (369-c)

Distribute the 5.8

1671 =3.25c +5.8*369 - 5.8c

1671 = 3.25c +2140.2-5.8c

Combine like terms

1671 = -2.55c +2140.2

Subtract 2140.2 from each side

1671-2140.2 = -2.55c +2140.2-2140.2

-469.2 = -2.55c

Divide by -2.55 on each side

-469.2/-2.55 = -2.55c/-2.55

184 =c

There were 184 children

Now we need to find a

369 = a+c

369 = a+184

Subtract 184 from each side

369-184 = a+184-184

185 =a

There were 185 adults