Question 1204605
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Pharrell and Justin are buying hot dogs and hamburgers for the football concession stand. 
Hotdogs (x) cost $2.50 each and hamburgers (y) cost $5.50 each. 
Pharrell would like to spend no more than $45.00 and Justin would like to have twice 
as many hot dogs as hamburgers and have more than 5 meals. 
Which is a viable solution for the system of inequalities?
A. (8,4)
B. (4,6)
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This problem includes one inequality &nbsp;&nbsp;2.50*x + 5.50*y <= 45  &nbsp;&nbsp;and one equation &nbsp;&nbsp;x = 2y.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It does not ask to find all possible solutions to given inequality and given equation..

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It also does not ask to find an optimal solution.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It &nbsp;ONLY &nbsp;asks to check if two given points on the coordinate plane &nbsp;(or two pairs of numbers)

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;satisfy the given inequality and the given equation.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, this problem is much easier than it may seem from the first glance.



<pre>
Step 1.  <U>Check if the pair (8,4) satisfies the given restrictions</U>


         The inequality is  2.50x + 5.50y <= 45.

         Substitute x=8, y= 4:  2.50*8 + 5.50*4 = 42 dollars.  This inequality is satisfied.


         The equation is x = 2y.

         Substitute x=8, y= 4:  8 = 2*4.  This equation is satisfied.


         Thus the pair (8,4) is the solution to the problem.    <U>ANSWER</U>



Step 2.  <U>Check if the pair (4,6) satisfies the given restrictions</U>


         The inequality is  2.50x + 5.50y <= 45.

         Substitute x=4, y= 6:  2.50*4 + 5.50*6 = 43 dollars.  This inequality is satisfied.


         The equation is x = 2y.

         Substitute x=4, y= 6:  4 =/= 2*6.  This equation is NOT satisfied.


         Hence, the pair (4,6) is NOT the solution to the problem.    <U>ANSWER</U>
</pre>

Solved, with explanations.