Simple question #10

A group of adults and kids went to see a movie. Tickets cost $7.00 each for adults and $4.50 each for kids, and the group paid $64.00 in total. There were 4 fewer adults than kids in the group.
Find the number of adults and kids in the group.

$\begin{array}{lrcl} a = \text{adults}\\ k = \text{kids}\\ \hline (1) & a\cdot $7.00 + k\cdot $4.50 &=& $64.00\\ (2) & a &=& k-4 \\ \hline & a\cdot $7.00 + k\cdot $4.50 &=& $64.00 \qquad | \qquad a &=& k-4\\ & (k-4)\cdot $7.00 + k\cdot $4.50 &=& $64.00\\ & k\cdot $7.00 -4\cdot $7.00 + k\cdot $4.50 &=& $64.00\\ & k\cdot $7.00 + k\cdot $4.50 -4\cdot $7.00&=& $64.00\\ & k\cdot $11.5 -4\cdot $7.00&=& $64.00 \\ & k\cdot $11.5 - $28.00&=& $64.00 \qquad | \qquad + $28.00\\ & k\cdot $11.5 &=& $64.00 + $28.00\\ & k\cdot $11.5 &=& $92.00 \qquad | \qquad : $11.5\\ & k &=& \frac{ $92.00}{ $11.5 } \\ & \mathbf{k} &\mathbf{=}& \mathbf{8} \\ \hline & a &=& k-4 \qquad | \qquad k = 8\\ & a &=& 8-4 \\ & \mathbf{a} &\mathbf{=}& \mathbf{4} \\ \end{array}$

The number of adults is 4

and the number of kids in the group is 8

x = number of adults.....then,

x + 4 = number of kids

then

x (7.00) + (x + 4) (4.50) = 64

7x + 4.5x + 18 = 64

11.5x = 46

x = 46/11.5 = number of adults = 4 adults