Question

Maya had $27. She spent all the money on buying 3 burgers for $x each and 2 sandwiches for $y each. If Maya would have 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).
b. The student's conclusion is incorrect because the solution to the system of equations 3x - 2y = 11 and 2x - y = 16 is (5, 6).
c. The student's conclusion is correct because the solution to the system of equations 3x + 2y = 27 and 2x + y = 16 is (5, 6).
d. The student's conclusion is incorrect because the solution to the system of equations 2x + 3y = 27 and x + 2y = 16 is (5, 6).

Answer 1

C is the correct answer. Solve for Y on the second equation, plug it in the other equation, and solve for x.

Answer 2

Answer:

Option C

The student's conclusion is correct because the solution to the system of equations $3x+2y=27$  and $2x+y=16$ is $(5,6)$

Step-by-step explanation:

Let

x------> the cost of each burger

y-----> the cost of each sandwich

we know that

$3x+2y=27$ -----> equation A

$2x+y=(27-11)$

$2x+y=16$ ----> equation B

Solve the system of equations

Multiply the equation B by $-2$

$-2(2x+y)=-2*16$ ----->$-4x-2y=-32$ ------> equation C

Adds equation A and equation C

$3x+2y=27 \\-4x-2y=-32\\ ----------\\ 3x-4x=27-32\\ -x=-5\\x=5$

Substitute the value of x in the equation B

$2(5)+y=16$

$10+y=16$

$y=6$

The solution of the system of equations is the point $(5,6)$

so

The price of each burger is $\ 5$

The price of each sandwich is $\ 6$