For his dog Bowser, Max mixes a 14 pound bag of gravy treat dog food with a 10 pound bag of hungry chops dog food. Then Max puts the mixture into small bags that each way 1 1/2 pounds. If the proportional relationship between the quantities of the two dog foods remain consent, how many pounds of gravy treat would each small bag contain?
The proportion of gravy:chops is 14:10 or 7:5
So, each bag contains
7/12 * 3/2 = 7/8 lbs of gravy treats
and
5/12 * 3/2 = 5/8 lbs of hungry chops
Thank you
To find out how many pounds of gravy treat dog food each small bag would contain, we need to determine the ratio of gravy treat dog food to the total mixture.
First, let's calculate the total weight of the mixture. Max mixes a 14-pound bag of gravy treat dog food with a 10-pound bag of hungry chops dog food:
Total weight of the mixture = 14 pounds + 10 pounds = 24 pounds
Now, let's find the ratio of gravy treat dog food to the total mixture:
Ratio of gravy treat dog food = weight of gravy treat dog food / total weight of the mixture
Ratio of gravy treat dog food = 14 pounds / 24 pounds
Ratio of gravy treat dog food = 7/12
Since each small bag weighs 1 1/2 pounds, we can find how many pounds of gravy treat dog food each small bag contains by multiplying the ratio by the weight of each small bag:
Pounds of gravy treat dog food per small bag = Ratio of gravy treat dog food * weight of each small bag
Pounds of gravy treat dog food per small bag = (7/12) * 1 1/2 pounds
To simplify the calculation, convert 1 1/2 pounds to an improper fraction:
1 1/2 = 3/3 + 1/2 = 6/2 + 1/2 = 7/2
Pounds of gravy treat dog food per small bag = (7/12) * (7/2) pounds
Now, multiply the numerators and the denominators:
Pounds of gravy treat dog food per small bag = (7 * 7) / (12 * 2) pounds
Pounds of gravy treat dog food per small bag = 49 / 24 pounds
Therefore, each small bag would contain approximately 2.042 pounds (rounded to three decimal places) of gravy treat dog food.
To find out how many pounds of gravy treat each small bag would contain, we need to determine the proportion of gravy treat dog food in the mixture.
Step 1: Find the total weight of the mixture
To find the total weight of the mixture, add the weight of the gravy treat dog food (14 pounds) with the weight of the hungry chops dog food (10 pounds).
Total weight = 14 pounds + 10 pounds = 24 pounds
Step 2: Find the proportion of gravy treat dog food in the mixture
To find the proportion of gravy treat dog food in the mixture, divide the weight of the gravy treat dog food by the total weight of the mixture.
Proportion of gravy treat = Weight of gravy treat dog food / Total weight of mixture
Proportion of gravy treat = 14 pounds / 24 pounds
Step 3: Find the weight of gravy treat in each small bag
To find the weight of gravy treat in each small bag, multiply the proportion of gravy treat by the weight of each small bag.
Weight of gravy treat in each small bag = Proportion of gravy treat * Weight of each small bag
Weight of gravy treat in each small bag = (14 pounds / 24 pounds) * 1 1/2 pounds
To simplify the fraction, convert the mixed number to an improper fraction:
1 1/2 pounds = 3/2 pounds
Weight of gravy treat in each small bag = (14/24) * (3/2) pounds
To perform the calculation, simplify the fraction and multiply:
Weight of gravy treat in each small bag = (7/12) * (3/2) pounds
Weight of gravy treat in each small bag = 21/24 pounds
So, each small bag would contain 21/24 pounds of gravy treat dog food.