Maya had $27. She spent all the money on buying 3 burgers for $x each and 2 sandwiches for $y each. If Maya had bought 2 burgers and 1 sandwich, she would have been left with $11.
A student concluded that the price of each burger is $5 and the price of each sandwich is $6. Which statement best justifies whether the student's conclusion is correct or incorrect?
The student's conclusion is correct because the solution to the system of equations 3x + 2y = 11 and 2x + y = 16 is (5, 6).
The student's conclusion is incorrect because the solution to the system of equations 3x − 2y = 11 and 2x − y = 16 is (5, 6).
The student's conclusion is correct because the solution to the system of equations 3x + 2y = 27 and 2x + y = 16 is (5, 6).
The student's conclusion is incorrect because the solution to the system of equations 2x + 3y = 27 and x + 2y = 16 is (5, 6).
3x + 2 y = 27
2 x + y = 27-11 = 16
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The student's conclusion is correct because the solution to the system of equations 3x + 2y = 27 and 2x + y = 16 is (5, 6). C
Now I did the other one. You do this one.
is it b
To determine whether the student's conclusion is correct or incorrect, we need to solve the given system of equations and compare the solution to the prices mentioned in the conclusion.
The given system of equations is:
3x + 2y = 11 ----(1)
2x + y = 16 ----(2)
First, let's solve the system of equations (1) and (2). We can use substitution or elimination method.
Using substitution method:
From equation (2), solve for x:
x = 16 - y
Substitute x into equation (1):
3(16 - y) + 2y = 11
48 - 3y + 2y = 11
48 - y = 11
-y = 11 - 48
-y = -37
Multiply the equation by -1 to make y positive:
y = 37
Substitute y = 37 into equation (2):
2x + 37 = 16
2x = 16 - 37
2x = -21
x = -21/2
Therefore, the solution to the system of equations (1) and (2) is (x, y) = (-21/2, 37).
Now, let's compare this solution to the conclusion's prices:
The conclusion states that the price of each burger is $5 and the price of each sandwich is $6.
The solution from the system of equations does not match the conclusion's prices. Therefore, the student's conclusion is incorrect.
Hence, the correct statement is: The student's conclusion is incorrect because the solution to the system of equations 3x + 2y = 11 and 2x + y = 16 is (-21/2, 37).