Question

The admission fee at an amusement park is $1.25 for children and $5.00 for adults. on a certain day, 312 people entered the park, and the admission fees collected totaled $840. how many children and how many adults were admitted?

Answer 1

120 Adult and 192 Child tickets

Explanation:

Let C and A stand for the numbers of Children (C) and Adults (A) tickets purchased.

The dollar amount sold for each group would be the number times the price per ticket for that group. Total sales would be:

Total($) = $1.25*C + $5*A, which we know is $840.

$840 = $1.25*C + $5*A

We also learn that C + A is 312 people total, which we'll write as:

C + A = 312

We have two equations and two unknowns, so we should be able to find an answer by using substitution. To start, lets rearrange the equation C + A = 312 to isolate either the C or A. Lets isolate C:

C + A = 312

C = 312 - A

Now use this definition of A in the first equation:

$840 = $1.25*C + $5*A

$840 = $1.25*(312 - A) + $5*A [Since C = (312 - A)]

$840 = $390 -$1.25A + $5*A

$450 = $3.75A

A = 120 adults

Since C = 312 - A

C = 312 - 120

C = 192

120 Adult and 192 Child tickets are sold.

CHECK:

Do 120 Adult and 192 Child tickets add to $840?

120*($5.00) + 312*($1.25) = $840

$240 + $600 = $840 ? YES