Roxie is a show dog her trainer wants her to have a beautiful and brilliant coat. The veterinarian suggested a special diet for the trainer to follow each feeding Roxie eats 2/3 of a can of wet dog foods 1/8 of a bag of dry food and 3/5 a patty of special meat the special meat comes in a package of 6 patties Roxie has two meals a day

Answer:  the answers are below

Step-by-step explanation:

1 meal = 2/3 of a can of wet dog food, 1/8 of a bag of dry dog food, and 3/5 a patty of special meat

Food for 1 day: 2 meals = 2(2/3) = 4/3 of a can of wet dog food, 2(1/8) = 1/4 of a bag of dry dog food, and 2(3/5) = 6/5 a patty of special meat

The trainer goes to the store and buys 24 cans of wet food, 4 bags of dry food and 3 packages of meat (3*6 = 18 patties)

He has:

there is wet food for: 24/(4/3) = 24*3/4 = 18 days

there is dry food for: 4/(1/4) = 4*4 = 16 days

there is special meat food for: 18/(6/5) = 18*5/6 = 15 days

since the minimum for 15, 16 and 18 is 15 the dog will have food for 15 days and first he will run out of special meat.

1. Roxie will be fed for 15 days before the trainer needs to buy more food.

2. The trainer will run out of the special meat first, as it will last for 15 days.

3. After the special meat runs out, there will be 3 cans of wet food and 1 bag of dry food left.

4. The trainer needs to buy 96 more cans of wet food, 19 more bags of dry food, and 36 more patties of special meat to last 90 days.

5. The minimum amount of food the trainer could buy is 80 cans of wet food, 15 bags of dry food, and 72 patties of special meat, which would last for 60 meals (30 days).

Step 1: Calculate the daily consumption of each type of dog food.

Wet food: 2/3 can per meal * 2 meals per day

= 4/3 cans per day.

Dry food: 1/8 bag per meal * 2 meals per day

= 1/4 bag per day.

Special meat: 3/5 patty per meal * 2 meals per day

= 6/5 patties per day.

Step 2: Calculate the total food available for Roxie.

Wet food: 24 cans purchased.

Dry food: 4 bags purchased.

Special meat: 3 packages (3 * 6 patties = 18 patties) purchased.

Step 3: Calculate the number of days the food will last.

Days of wet food: 24 cans / (4/3 cans per day)

= 24 * 3/4

= 18 days.

Days of dry food: 4 bags / (1/4 bag per day)

= 4 * 4

= 16 days.

Days of special meat: 18 patties / (6/5 patties per day)

= 18 * 5/6

= 15 days.

Step 4: Determine which type of dog food will run out first.

The special meat will run out first, after 15 days.

Step 5: Calculate how much of the other two types of dog food will be left after the first type runs out.

After 15 days, Roxie will still have

= 18 - 15

= 3 cans of wet food left.

After 15 days, Roxie will still have

=  16 - 15

= 1 bag of dry food left.

Step 6: Plan for 90 days.

The total number of patties needed for 90 days

= (6/5 patties per day) * 90 days

= 108 patties.

and, the trainer needs to buy

=  108 / 6 = 18 packages

- For wet food, Roxie needs

=  (4/3 cans per day) * 90 days

= 120 cans.

The trainer already has 24 cans, so she needs to buy

= 120 - 24 = 96 more cans.

- For dry food, Roxie needs

=  (1/4 bag per day) * 90 days = 22.5 bags.

Since the trainer can't buy half a bag, she needs to round up to 23 bags.

Step 7: Minimum amount of food to buy to finish all of it after a certain number of meals.

Minimum amount of wet food to buy:

= (4/3 cans per day) * 60

= 80 cans.

Minimum amount of dry food to buy:

=(1/4 bag per day) * 60

= 15 bags.

Minimum amount of special meat to buy:

=(6/5 patties per day) * 60

= 72 patties.

Therefore, the trainer could buy a minimum of 80 cans of wet food, 15 bags of dry food, and 72 patties of special meat, and Roxie would finish all of it after 60 meals (30 days).

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