To solve the equation [tex]\(\frac{2}{3}=\frac{x}{6}=\frac{y}{24}=\frac{20}{z}\)[/tex], we need to find the values of [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(z\)[/tex]:
1. Finding [tex]\(x\)[/tex] for [tex]\(\frac{2}{3} = \frac{x}{6}\)[/tex]:
- By cross-multiplying, we get: [tex]\(2 \times 6 = 3 \times x\)[/tex].
- This simplifies to: [tex]\(12 = 3x\)[/tex].
- Solving for [tex]\(x\)[/tex], we get: [tex]\(x = \frac{12}{3} = 4\)[/tex].
2. Finding [tex]\(y\)[/tex] for [tex]\(\frac{2}{3} = \frac{y}{24}\)[/tex]:
- By cross-multiplying, we get: [tex]\(2 \times 24 = 3 \times y\)[/tex].
- This simplifies to: [tex]\(48 = 3y\)[/tex].
- Solving for [tex]\(y\)[/tex], we get: [tex]\(y = \frac{48}{3} = 16\)[/tex].
3. Finding [tex]\(z\)[/tex] for [tex]\(\frac{2}{3} = \frac{20}{z}\)[/tex]:
- By cross-multiplying, we get: [tex]\(2 \times z = 3 \times 20\)[/tex].
- This simplifies to: [tex]\(2z = 60\)[/tex].
- Solving for [tex]\(z\)[/tex], we get: [tex]\(z = \frac{60}{2} = 30\)[/tex].
So, we have the values:
[tex]\[ x = 4, \][/tex]
[tex]\[ y = 16, \][/tex]
[tex]\[ z = 30. \][/tex]
Therefore, the completed equation is:
[tex]\[ \frac{2}{3} = \frac{4}{6} = \frac{16}{24} = \frac{20}{30}. \][/tex]
