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
\(\frac{x}{y}=\frac{8}{15}\)
\(\frac{8}{15}
eq \frac{2}{3}\)
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 \(2:3:4\)
