Question

The mass of a liquid varies directly with its volume. A liquid with mass 16 kilograms has a volume of 2 liters.

a. Write the equation that relates the mass to the volume.

b. What is the volume of this liquid if its mass is 128 kilograms?

Short answer

a. The equation relating mass and volume is $m=8v$.

b. For 128 kilograms mass, volume of the liquid is 2 liters.

Step-by-step solution

Part (a). Step 1. Given information

From the given information, the mass$m$is 16 kilograms and volume$v$is 2 liters.

Part (a). Step 2. Formula of direct variation

Substitute $m$for $y$and $v$for $x$into the formula of direct variation $y=kx$.

$m=kv$

Part (a). Step 3. Determine the equation relating m and v.

Substitute the given values into $m=kv$and solve for $k$.

$\begin{array}{rcl}16& =& k·2\\ \frac{16}{2}& =& k\\ 8& =& k\end{array}$

Substitute 8 for $k$into $m=kv$to obtain the equation relating $m$and $v$.

$m=8v$

Part (b). Step 1. Determine the volume for 128 kilograms mass.

Substitute 128 for $m$into $m=8v$and solve for $v$.

$\begin{array}{rcl}128& =& 8v\\ \frac{128}{8}& =& v\\ 16& =& v\end{array}$

So, the volume is 16 liters for 128 kilograms mass.