Question

Which of the following does not have a ratio of 2:3:4?

A) {8, 15, 24}
B) {2x, 3x, 4x}
C) {6m2, 9m2, 12m2}

Answer 1

8, 15, 24 because their simplified forms are not 234

Answer 2

`{8, 15, 24}`

Explanation:

In this problem we have a ratio with
`3` numbers

so

Let

x------> the first number

y-----> the second number

z-----> the third number

we know that

`(x)/(y)=(2)/(3)` ------> equation A

`(x)/(z)=(2)/(4)` ------> equation B

`(y)/(z)=(3)/(4)` ------> equation C

Verify each case

case A)
`{8, 15, 24}`

`x=8, y=15,z=24`

Substitute in the equations

`(x)/(y)=(8)/(15)`

`(8)/(15)\\eq (2)/(3)`

therefore

The case A) not have a ratio of
`2:3:4`

case B)
`{2x,3x,4x}`

`x=2x, y=3x,z=4x`

Substitute in the equations

`(x)/(y)=(2x)/(3x)=(2)/(3)`

`(x)/(z)=(2x)/(4x)=(2)/(4)`

`(y)/(z)=(3x)/(4x)=(3)/(4)`

therefore

The case B) have a ratio of
`2:3:4`

case C)
`{6m^(2),9m^(2),12m^(2)}`

`x=6m^(2), y=9m^(2),z=12m^(2)`

Substitute in the equations

`(x)/(y)=(6m^(2))/(9m^(2))=(2)/(3)`

`(x)/(z)=(6m^(2))/(12m^(2))=(2)/(4)`

`(y)/(z)=(9m^(2))/(12m^(2))=(3)/(4)`

therefore

The case C) have a ratio of
`2:3:4`