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If (x)/(y)=(3)/(8) and (y)/(z)=(2)/(15) Then (x)/(z)=

If xy=38 \frac{x}{y}=\frac{3}{8} and yz=215 \frac{y}{z}=\frac{2}{15} \newlineThen xz= \frac{x}{z}=

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Q. If xy=38 \frac{x}{y}=\frac{3}{8} and yz=215 \frac{y}{z}=\frac{2}{15} \newlineThen xz= \frac{x}{z}=
  1. Express xx in terms of yy: Given the ratio xy=38\frac{x}{y} = \frac{3}{8}, we can express xx in terms of yy as x=3y8x = \frac{3y}{8}.
  2. Express yy in terms of zz: Similarly, given the ratio yz=215\frac{y}{z} = \frac{2}{15}, we can express yy in terms of zz as y=2z15y = \frac{2z}{15}.
  3. Find xx in terms of zz: Now, we substitute the expression for yy from the second equation into the first equation to find xx in terms of zz. So, x=3×(2z15)8x = \frac{3 \times \left(\frac{2z}{15}\right)}{8}.
  4. Simplify xx expression: Simplify the expression for xx in terms of zz by multiplying the numerators and denominators: x=3×2z8×15x = \frac{3 \times 2z}{8 \times 15}.
  5. Further simplify xx: Further simplify the expression: x=6z120x = \frac{6z}{120}.
  6. Reduce xx fraction: Reduce the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 66: x=z20x = \frac{z}{20}.

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