One gallon of liquid occupies 231 cubic inches. Write a rule that expresses the number of gallons g(c) as a function of the number of cubic inches c.
Choices are:
g(c)=c/231
g(c)=132/c
g(c)=231c
g(c)=132c
g(c)=c/231
The rule that expresses the number of gallons g(c) as a function of the number of cubic inches c is g(c) = c/231.
To understand how this rule is derived, we can observe the given information that one gallon of liquid occupies 231 cubic inches. This means that for every gallon of liquid, we have 231 cubic inches.
To express this relationship mathematically, we can set up a proportionality equation:
1 gallon is to 231 cubic inches as g gallons is to c cubic inches.
Mathematically, this can be written as:
1/231 = g/c.
To solve for g, we can cross-multiply:
1 * c = 231 * g.
Simplifying this equation, we get:
c = 231g.
To isolate g, we divide both sides of the equation by 231:
g = c/231.
Therefore, the rule that expresses the number of gallons g(c) as a function of the number of cubic inches c is g(c) = c/231.