Question

Help me with this question

Answer 1

The correct option is: x > z

Hence, option D is correct.

Explanation:

Given

• 
  `(3y+1)/(2)=5`

• 
  `\:(4x)/(3)=8`

• 
  `(z)/(3)+(z)/(4)=2`

solving

`(3y+1)/(2)=5`

Multiply both sides by 2

`(2\left(3y+1\right))/(2)=5\cdot \:2`

Simplify

`3y+1=10`

Subtract 1 from both sides

`3y+1-1=10-1`

Simplify

`3y=9`

Divide both sides by 3

`(3y)/(3)=(9)/(3)`

Simplify

`y=3`

also solving

`\:(4x)/(3)=8`

Multiply both sides by 3

`(3\cdot \:4x)/(3)=8\cdot \:3`

`4x=24`

Divide both sides by 4

`(4x)/(4)=(24)/(4)`

Simplify

`x=6`

also solving

`(z)/(3)+(z)/(4)=2`

Multiply by L.C.M

`(z)/(3)\cdot \:12+(z)/(4)\cdot \:12=2\cdot \:12`

Simplify

`4z+3z=24`

`7z=24`

Divide both sides by 7

`(7z)/(7)=(24)/(7)`

Simplify

`z=(24)/(7)`

`z=3.4`

Thus,

`y=3`

`x=6`

`z=3.4`

so

x > z

Therefore, the correct option is: x > z

Hence, option D is correct.