Carlos purchased 6 dog leashes and 6 cat brushes for $45.00 for Clarita to use while

pampering the pets. Later in the summer he purchased 3 additional dog leashes and 2 cat
brushes for $19.00. Based on this information, figure out the price of each item. Explain
your reasoning.

Well, Carlos seems quite committed to pampering the pets. Let's calculate the price of each item, shall we?

First, let's tackle the 6 dog leashes and 6 cat brushes that cost $45.00. Since both items are mentioned together, we know these prices are related.

Let's assume the price of a dog leash is "D" and the price of a cat brush is "C". So, we have the equation:
6D + 6C = 45.00

Next, Carlos purchases 3 additional dog leashes and 2 cat brushes for $19.00. Using the same logic, we have:
3D + 2C = 19.00

Now we have a system of equations! To solve it, we can use either substitution or elimination methods. Let's go with the substitution method.

From the second equation, let's solve for D:
3D = 19 - 2C
D = (19 - 2C)/3

Now, let's substitute this value of D into the first equation:
6((19 - 2C)/3) + 6C = 45

Simplifying further, we obtain:
12 - 4C + 6C = 45
2C = 33
C = 16.50

Now that we have the price of a cat brush, let's substitute it back into the second equation:
3D + 2(16.50) = 19
3D + 33 = 19
3D = -14
D = -4.67

Now, since we cannot have negative prices, we made an error somewhere. We might have to reconsider our reasoning or double-check the information given.

Let's break down the information given step-by-step:

Step 1: Calculate the total cost of the initial purchase
Carlos purchased 6 dog leashes and 6 cat brushes for a total of $45.00.
Let's assume the price of each dog leash is "x" and the price of each cat brush is "y".
So, the total cost of the initial purchase can be calculated as follows:
6x + 6y = $45.00 ----(Equation 1)

Step 2: Calculate the total cost of the second purchase
Carlos purchased 3 additional dog leashes and 2 cat brushes for a total of $19.00.
Using the same assumption, the total cost of the second purchase can be calculated as follows:
3x + 2y = $19.00 ----(Equation 2)

Step 3: Solve the system of equations
To find the price of each item, we need to solve the system of equations formed by Equation 1 and Equation 2.

Equation 1: 6x + 6y = $45.00
Equation 2: 3x + 2y = $19.00

We can solve this system of equations using elimination or substitution method.

Using the elimination method, we can multiply Equation 2 by 2 and Equation 1 by -3 to cancel out the y term:
-3(6x + 6y) = -3($45.00) ----(Equation 1 multiplied by -3)
2(3x + 2y) = 2($19.00) ----(Equation 2 multiplied by 2)

Simplifying these equations, we get:
-18x - 18y = -$135.00
6x + 4y = $38.00

Adding the two equations, we have:
-18x - 18y + 6x + 4y = -$135.00 + $38.00
-12x - 14y = -$97.00

Now, we can solve for x or y by isolating one variable. Let's solve for x:

-12x = -14y - $97.00
x = (-14y - $97.00) / -12

Now, substitute the value of x in Equation 2 and solve for y:

3((-14y - $97.00) / -12) + 2y = $19.00

Simplifying this equation, we get:
-14y - $97.00 + 2y = $19.00
-12y - $97.00 = $19.00

Solving for y, we have:
-12y = $19.00 + $97.00
-12y = $116.00
y = $116.00 / -12
y = -$9.67

Now, substitute the value of y in Equation 1 and solve for x:

6x + 6(-$9.67) = $45.00
6x - $58.02 = $45.00
6x = $45.00 + $58.02
6x = $103.02
x = $103.02 / 6
x = $17.17

Therefore, the price of each dog leash is $17.17, and the price of each cat brush is -$9.67.
(Note: The negative value of the cat brush suggests a potential error in the calculation or the given information, as prices cannot be negative.)

To figure out the price of each item, we can set up a system of equations based on the given information.

Let's assume the price of a dog leash is represented by d and the price of a cat brush is represented by c.

From the first purchase:
Carlos purchased 6 dog leashes and 6 cat brushes for $45.00.
This can be represented by the equation: 6d + 6c = 45.00

From the second purchase:
Carlos purchased 3 additional dog leashes and 2 cat brushes for $19.00.
This can be represented by the equation: 3d + 2c = 19.00

Now we have a system of equations:
6d + 6c = 45.00
3d + 2c = 19.00

We can solve this system of equations to find the values of d and c. There are several methods to solve this, such as substitution or elimination. Let's use the elimination method in this example.

First, let's multiply the second equation by 2 to eliminate the c term:
2 * (3d + 2c) = 2 * 19.00
6d + 4c = 38.00

Now we have the following system of equations:
6d + 6c = 45.00
6d + 4c = 38.00

Next, subtract the second equation from the first equation to eliminate the d term:
(6d + 6c) - (6d + 4c) = 45.00 - 38.00
2c = 7.00

Divide both sides of the equation by 2 to solve for c:
c = 7.00 / 2
c = 3.50

Now we have found the value of c, which represents the price of a cat brush.

To find the value of d, plug the value of c back into one of the original equations. Let's use the first equation:
6d + 6c = 45.00
6d + 6(3.50) = 45.00
6d + 21.00 = 45.00

Subtract 21.00 from both sides of the equation:
6d = 45.00 - 21.00
6d = 24.00

Divide both sides of the equation by 6 to solve for d:
d = 24.00 / 6
d = 4.00

Therefore, the price of each dog leash is $4.00 and the price of each cat brush is $3.50.

6 + 6 = 12

45 / 12 = 3.75
3 + 2 = 5
5 x 3.75 = 18.75

round 18.75, it'll be 19.

so the price of each item, most probably, is 3.75.