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

the answer is c he is wright

Explanation:

Answer 2

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)`

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`