A group of students volunteers at the animal it helping feeds the dogs. Each day small dogs eat 1/2 cup less dog food than medium sized dogs and large dogs eat 3/4 cup more dog food than the medium sized dogs. The shelter currently has 22 small dogs, 14 medium sides dogs and 8 large dogs.
Write and expression for the total amount of dog food the dogs eat each day, explaining what your variabl represents and what each term in your expression represents.
Medium sized dogs eat X cups/day.
Small dogs eat x-1/2 cups/day.
Large dogs eat x+3/4 cups/day.
Total = x + (x-1/2) + (x+3/4) = 3x-1/2+3/4 = 3x-2/4+3/4 = 3x + 1/4 cups/day.
To write an expression for the total amount of dog food the dogs eat each day, we need to consider the amount of dog food eaten by each size category of dogs: small, medium, and large.
Let's start by defining some variables:
- Let's represent the amount of dog food eaten by small dogs as "S."
- The amount of dog food eaten by medium-sized dogs will be represented as "M."
- Finally, the amount of dog food eaten by large dogs will be represented as "L."
Given that small dogs eat 1/2 cup less dog food than medium-sized dogs, we can represent this as:
S = M - 1/2
Similarly, if large dogs eat 3/4 cup more dog food than medium-sized dogs, we can represent it as:
L = M + 3/4
Now, we can calculate the total amount of dog food eaten each day by all the dogs in the shelter:
Total = (S + M + L) * (number of small dogs + number of medium-sized dogs + number of large dogs)
Substituting the values for the number of dogs in each category:
- The number of small dogs is 22
- The number of medium-sized dogs is 14
- The number of large dogs is 8
The expression becomes:
Total = (S + M + L) * (22 + 14 + 8)
Since we now have expressions for S, M, and L in terms of M, we can simplify this equation further by substituting the values of S and L:
Total = ((M - 1/2) + M + (M + 3/4)) * (22 + 14 + 8)
Now, you can simplify the expression by combining like terms and compute the total amount of dog food the dogs eat each day.