Question

The value of y varied jointly with x and z. If y=2 when z=110 and x=11, find the appropriate value of y when x=13 and z=195.

Answer 1

Given the ratio:

$\text{ x : y : z }\rightarrow\text{ 11 : 2 : 110}$

To be able to get the value of y at x = 13 and z = 195, let's recall how this ratio transforms into an equation:

At x : y : z

$\frac{x}{xyz}=\frac{y}{xyz}=\frac{z}{xyz}$

Let's now plugin the values to be able to find the value of y:

$\frac{2}{(11)(2)(110)}=\frac{13}{(13)(y)(195)}$

Let's simplify the equation:

$\frac{2}{(11)(2)(110)}=\frac{13}{(13)(y)(195)}\text{ }\rightarrow\text{ }\frac{2}{2420}=\frac{13}{2535y}$$2(2,535y)=13(2,420)$$5,070y\text{ = 31,460}$$\frac{5,070y}{5070}\text{ = }\frac{\text{31,460}}{5070}$$\text{ y = 6.2}05\text{ }\approx\text{ 6.21}$

Therefore, y = 6.21