You can make 5
gal of liquid fertilizer by mixing 12
tsp of powdered fertilizer with water. Represent the relation between the teaspoons of powder used and the gallons of fertilizer made using a table, an equation, and a graph. Is the amount of fertilizer made a function of the amount of powder used?
Question content area bottom
Part 1
Which table below represents the relation?
A.
Number of gal, x
Number of tsp, y
0
15
12
10
24
5
36
0
Your answer is not correct.
B.
Number of tsp, x
Number of gal, y
0
0
5
12
10
24
15
36
C.
Number of tsp, x
Number of gal, y
0
0
12
5
24
10
36
15
This is the correct answer.
Part 2
Represent the relation using an equation.
yequals
enter your response here
(Simplify your answer. Type an expression using x as the variable. Use integers or fractions for any numbers in the expression.)
Part 1:
The correct table is option C, because it represents the direct relation between the number of teaspoons of powdered fertilizer used (x) and the number of gallons of liquid fertilizer made (y). It indicates that for every 12 teaspoons of powder, we can make 5 gallons of liquid fertilizer.
The table is:
Number of tsp, x | Number of gal, y
-----------------|-----------------
0 | 0
12 | 5
24 | 10
36 | 15
Part 2:
To represent the relation using an equation, we need to establish the rate of conversion from teaspoons to gallons. Since 12 tsp makes 5 gal, we can set up a proportion to find the number of gallons (y) for any number of teaspoons (x):
12 tsp / 5 gal = x tsp / y gal
Solving this proportion for y, we get:
y = (5 gal / 12 tsp) * x
Therefore, the equation representing the relation between the number of teaspoons (x) and the number of gallons of liquid fertilizer (y) is:
y = (5/12)x
Yes, the amount of fertilizer made is a function of the amount of powder used. In this case, for each input value of the amount of powder, there is exactly one output value of the amount of fertilizer, which satisfies the definition of a function.