Use proportional reasoning to solve the following problems.  

1. A typical small bag of colored candies has about $135$ candies in it, $27$ of which are blue. At this rate, how many blue candies would you expect in a pile of $1000$ colored candies?

   Hint (a):

   Use proportions to set up the problem.

   $\frac{27\text{ blue}}{135\text{total}} = \frac{n}{1000\text{ total}}$

   $27\cdot 1000=135 \cdot n$

   $\frac{27000}{135}=\frac{135n}{135}$

   Answer (a):

   $n=200$

2. Ten calculators cost $\$149.50$. How much would $100$ cost? $1000$? $500$?

   Hint (b):

   Use proportions to set up the problem.

   $\frac{10}{149.50}=\frac{100}{n}$

   More Help (b):

   Multiply by a fraction equal to $1$ in order to make the equivalent proportions have exactly similar numbers.

   $\frac{10}{149.50}\cdot \frac{10}{10}=\frac{100}{n}$

   Solve for $n$ by multiplying $149.50$ by $10$.

   Answer (b):

   $n=\$1495$

3. Tickets to $50$ home baseball games would cost $\$1137.50$. How much would it cost to get tickets for all $81$ home games? How many games could you go to for $\$728$?

   Hint (c):

   Use the strategy seen in part (a).