# Question ff115

$52. #### Explanation: There are $4$persons in the Group. To purchase a ticket, one has to pay$7.25.
$\therefore \text{ cost of 4 tickets } = 4 \left(7.25\right) \ldots . \left(1\right)$
To purchase a drink & popcorn, one has to pay $5.75. $\therefore \text{ cost of the refreshment for 4 friends} = 4 \left(5.75\right) \ldots . \left(2\right)$Clearly, to get the total cost for the group of 4 friends, we have to add (1) & (2), i.e., $\text{The total cost=} 4 \left(7.25\right) + 4 \left(5.75\right) \ldots \ldots \ldots \left(\star\right)$Now, here comes the Maths. to save your labour! A Well-known Property of Numbers, called "The Distributive Property" says that, $a \left(b + c\right) = a \cdot b + a \cdot c ,$or, taking the other way round, $a \cdot b + a \cdot c = a \left(b + c\right)$Observe that, to get the total cost from $\left(\star\right)$, we have to perform multiplication twice, but, by the Distributive Property as shown in the last eqn., we have to multiply only once. $\text{So, the total cost=} 4 \left(7.25\right) + 4 \left(5.75\right) = 4 \left(7.25 + 5.75\right) = 4 \left(13.00\right)$, "i.e.,"=$52#.