Question

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

Answer 1

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

Answer 2

Answer:

${8, 15, 24}$

Step-by-step 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

$\frac{x}{y}=\frac{2}{3}$ ------> equation A

$\frac{x}{z}=\frac{2}{4}$ ------> equation B

$\frac{y}{z}=\frac{3}{4}$ ------> equation C

Verify each case

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

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

Substitute in the equations

$\frac{x}{y}=\frac{8}{15}$

$\frac{8}{15}\neq \frac{2}{3}$

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

$\frac{x}{y}=\frac{2x}{3x}=\frac{2}{3}$  

$\frac{x}{z}=\frac{2x}{4x}=\frac{2}{4}$

$\frac{y}{z}=\frac{3x}{4x}=\frac{3}{4}$

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

$\frac{x}{y}=\frac{6m^{2}}{9m^{2}}=\frac{2}{3}$  

$\frac{x}{z}=\frac{6m^{2}}{12m^{2}}=\frac{2}{4}$

$\frac{y}{z}=\frac{9m^{2}}{12m^{2}}=\frac{3}{4}$

therefore

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