Margie is responsible for buying a week's supply of food and medication for the dogs and cats at a local shelter. The food and medication for each dog costs twice as much as those supplies for a cat. She needs to feed 164 cats and 24 dogs. Her budget is K4,240. How much can Margie spend on each dog for food and medication?
cost of cat --- x
cost for dog -- 2x
164x + 24(2x) = 4240
212x = 4240
x = 20
spends 20 on a cat and 40 on a dog
check:
20(164) + 40(24) = 4240
Let's assume that the cost of supplies for each cat is X.
Given that the cost of supplies for each dog is twice the cost for a cat, the cost for each dog is 2X.
Margie needs to buy supplies for 164 cats at a cost of X each, so the total cost for cat supplies is 164X.
Similarly, she needs to buy supplies for 24 dogs at a cost of 2X each, so the total cost for dog supplies is 24 * 2X = 48X.
Margie's budget is K4,240, so she needs to find the value of X that satisfies the equation 164X + 48X = K4,240.
Combining like terms, we get 212X = K4,240.
Dividing both sides of the equation by 212, we find X = K20.
Now that we know the cost of supplies for each cat (X = K20), we can calculate the cost for each dog, which is twice the cost for a cat. So, the cost for each dog is 2 * K20 = K40.
Therefore, Margie can spend K40 on each dog for food and medication.
To find out how much Margie can spend on each dog for food and medication, we need to perform the following steps:
Step 1: Assign variables
Let's assign variables to the unknowns in the problem:
Let C be the cost of food and medication for a cat.
Since the cost for dogs is twice as much as cats, let D be the cost for food and medication for a dog, which is 2C.
Step 2: Find the total cost for cats
Since Margie needs to feed 164 cats, the total cost for cat supplies can be calculated by multiplying the cost per cat (C) by the number of cats (164):
Total cost for cat supplies = C * 164
Step 3: Find the total cost for dogs
Since Margie needs to feed 24 dogs and the cost for dogs is twice that of cats, the total cost for dog supplies can be calculated by multiplying the cost per dog (D) by the number of dogs (24):
Total cost for dog supplies = D * 24 = (2C) * 24 = 48C
Step 4: Write the equation
The total cost for cat supplies plus the total cost for dog supplies should equal Margie's budget. Therefore, we can set up the equation:
Total cost for cat supplies + Total cost for dog supplies = Margie's budget
C * 164 + 48C = K4,240
Step 5: Solve for C
Combine like terms:
164C + 48C = K4,240
212C = K4,240
Divide both sides of the equation by 212 to solve for C:
C = K4,240 รท 212
C = K20
Step 6: Calculate the cost for dogs
Since we know that D (cost for a dog) is twice the cost of a cat, we can calculate D:
D = 2C = 2 * K20 = K40
Therefore, Margie can spend K40 on each dog for food and medication.