Question

Compare cups of dried fruit to cups of sunflower seeds in the granola recipe.

The relationship between adult dog weight x in pounds and the daily recommended amount of dog food y in cups is proportional.
A table with two rows is shown. The first row is Dog weight in pounds and the second row is Dog food in cups. Ten pounds, one sixth cup. Forty pounds, two thirds cup. Fifty pounds, five sixths cup. One hundred pounds, one and two thirds cups.
A photo shows a large and small dog sitting side by side.
Write an equation for the relationship. How much dog food is recommended for a 25-pound adult dog?

Answer 1

The proportional relationship between dog weight and dog food can be expressed as y = (1/60)x. Using this equation, it's calculated that the recommended amount of dog food for a 25-pound dog is 5/12 cups.

Step-by-step explanation:

The relationship between an adult dog's weight (x in pounds) and the daily recommended amount of dog food (y in cups) is proportional. To find the equation for this relationship, we can use the given data points from the exercise. We know that a 10-pound dog requires 1/6 cup of food and a 100-pound dog requires 1 and 2/3 cups (which is equivalent to 5/3 cups).

First, we represent the proportionality constant as k, so our equation takes the form y = kx. Using our data points, we can solve for k

Solving either equation for k gives us the same result, k = 1/60. Thus, our equation relating dog weight to food amount is y = (1/60)x. To find out how much food is recommended for a 25-pound dog, we substitute x with 25:

y = (1/60)(25) = 5/12 cups

Therefore, the recommended amount of dog food for a 25-pound adult dog is 5/12 cups.