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Question 1204605: 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)
Answer by ikleyn(52818)   (Show Source):
You can put this solution on YOUR website! .
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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This problem includes one inequality 2.50*x + 5.50*y <= 45 and one equation x = 2y.
It does not ask to find all possible solutions to given inequality and given equation..
It also does not ask to find an optimal solution.
It ONLY asks to check if two given points on the coordinate plane (or two pairs of numbers)
satisfy the given inequality and the given equation.
So, this problem is much easier than it may seem from the first glance.
Step 1. Check if the pair (8,4) satisfies the given restrictions
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. ANSWER
Step 2. Check if the pair (4,6) satisfies the given restrictions
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. ANSWER
Solved, with explanations.
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