The 5/12 cups of dog food are recommended for a 25-pound adult dog
Step-by-step explanation:
Given:
The relationship between the weight of the adult dog (X) and the amount of dog food in cups (Y) is proportional.
To find:
Dog food for the 25-pound adult dog
Solution:
The weight of the adult dog (X) is proportional to the amount of dog food in cups are proportional.
[tex]X\propto Y\\\text{The equation for the relationship will be given as :}\\X=kY\\k=\frac{X}{Y}= Constant[/tex]
From the table given, we can calculate the value of the constant k.
[tex]k=\frac{10}{\frac{1}{6}}=\frac{40}{\frac{2}{3}}=\frac{50}{\frac{5}{6}}=\frac{100}{1\frac{2}{3}}\\k=\frac{10}{\frac{1}{6}}=\frac{40}{\frac{2}{3}}=\frac{50}{\frac{5}{6}}=\frac{100}{\frac{5}{3}}\\k=\frac{60}{1}=\frac{40\times 3}{2}=\frac{50\times 6}{50}=\frac{100\times 3}{5}\\k=60[/tex]
Let the dog food recommended for the 25-pound adult dog be y.
Weight of the dog = x = 25 pounds
Cups of dog food recommended = y
k = 60
Using the equation for the given relationship:
[tex]25=60\times y\\y=\frac{25}{60}=\frac{5}{12}[/tex]
The 5/12 cups of dog food are recommended for a 25-pound adult dog.
Learn more about direct proportion here:
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