Question

The admission for a school play is $2.25 for children and $8.50 for adults. On a certain day, 334 peopleattended the play, and the total money collected from sales was $1814. How many children and howmany adults were admitted?children attended.adults attended.

Answer 1

It is given that the admission for a school play is $2.25 for children and $8.50 for adults.

Let x be the number of children and y be the number of adults that attended.

It is also given that 334 people attended the play so it follows:

$x+y=334\ldots(i)$

It is also given that the total money collected from sales was $1814 so it follows:

$2.25x+8.50y=1814\ldots(ii)$

Multiply the first equation by 2.25 to get:

$2.25x+2.25y=751.5\ldots(iii)$

Subtract (iii) from (ii) to get:

$\begin{gathered} 2.25x+8.50y=1814 \\ - \\ 2.25x+2.25y=751.5 \\ 6.25y=1062.5 \\ y=170 \end{gathered}$

Substitute y=170 in (i) to get:

$\begin{gathered} x+170=334 \\ x=164 \end{gathered}$

Hence, it follows:

Children attended 164

Adults attended 170