Question

One quart is equivalent to 0.95 liter.

Answer 1

$\text{Answer: a) }x=0.95y$

$b)\ x=3.76y$

$c)\ x=1.05y$

$d)\ k_2=1.11\times k_1$

Explanation:

Since we have given that

$1\ quarts=0.95\ liters$

a) Write a direct variation equation that relates x quarts to y liters.

Since Direct variation can be written in the form :

$\frac{x}{y}=k\\\\x=yk\\\\x=0.95y\\\\Here,\ k=0.95$

b) Write a direct variation equation that relates x gallons to y liters.

Since we have given that

$1\ gallon=3.76\ liters$

Since Direct variation can be written in the form :

$\frac{x}{y}=k\\\\x=yk\\\\x=3.76y\\\\Here,\ k=3.76$

c) Write a direct variation equation that relates x liters to y quarts.

Since we have given that

$1\ liter=1.05\ quarts$

Since Direct variation can be written in the form :

$\frac{x}{y}=k\\\\x=yk\\\\x=1.05y\\\\Here,\ k=1.05$

d) What is the relationship between the values of k in the direct variation equations in parts (a) and (c)?

$\text{ let }k_1=0.95\text{ and }k_2=1.05\\\\k_2=1.11\times k_1$