Question

One quart is equivalent to 0.95 liter.

a. Write a direct variation equation that relates x quarts to y liters.
b. Write a direct variation equation that relates x gallons to y liters.
c. Write a direct variation equation that relates x liters to y quarts.
d. What is the relationship between the values of k in the direct variation equations in parts (a) and (c)?

Answer 1

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

`b)\ x=3.76y`

`c)\ x=1.05y`

`d)\ k_2=1.11* k_1`

Step-by-step 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 :

`(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 :

`(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 :

`(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* k_1`