Question

Any help, I would highly appreciate it ​

Answer 1

B

Explanation:

We are given the equation:

`\displaystyle x(b-c) = y+x`

And that:

`2b=3c=7`

And we want to find the value of y / x.

To start, subtract x from both sides in the first equation:

`x(b-c) -x = y`

Divide both sides by x:

`\displaystyle (x(b-c)-x)/(x)=(y)/(x)`

Simplify:

`\displaystyle (b-c)-1 = (y)/(x)`

Next, in the second equation, divide everything by two:

`\displaystyle b = (3)/(2) c = (7)/(2)`

Substitute:

`\displaystyle \left((3)/(2) c - c \right) - 1= (y)/(x)`

Simplify:

`\displaystyle (1)/(2) c - 1 = (y)/(x)`

From the modified second equation, we can multipy both sides by 1/3:

`\displaystyle (1)/(2) c = (7)/(6)`

Substitute:

`\displaystyle \left((7)/(6)\right) -1 = (y)/(x)`

Subtract:

`\displaystyle (y)/(x) = (7)/(6) - (6)/(6) = (1)/(6)`

Therefore, our answer is B.