# X and Y

• November 7th 2006, 03:40 PM
Dragon
X and Y
Suppose that
x/y= 4/7
And that y/z=14/3

What is the value of x+y/z

• November 7th 2006, 03:56 PM
Soroban
Hello, Dragon!

Quote:

Suppose that: $\frac{x}{y} = \frac{4}{7}$ and $\frac{y}{z} = \frac{14}{3}$

What is the value of $\frac{x + y}{z}$ ?

Multiply the two equations: . $\frac{x}{y}\cdot\frac{y}{z}\:=\:\frac{4}{7}\cdot\f rac{14}{3}\quad\Rightarrow\quad\frac{x}{z} = \frac{8}{3}$

So we have: . $\frac{x}{z} = \frac{8}{3}$ and $\frac{y}{z} = \frac{14}{3}$

Add these two equations: . $\frac{x}{z} + \frac{y}{z} \:=\:\frac{8}{3} + \frac{14}{3}\quad\Rightarrow\quad\boxed{\frac{x+y} {z} \:=\:\frac{22}{3}}$