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.
6L + 6B = 45
3L + 2B = 19
Solve the two equations for L and B, which are the price of leashes and brushes, respectively.
To figure out the price of each item, we can set up a system of equations using the given information.
Let's say the price of a dog leash is represented by 'x' dollars, and the price of a cat brush is represented by 'y' dollars.
From the first part of the problem, Carlos purchased 6 dog leashes and 6 cat brushes for a total of $45. So we can write the equation:
6x + 6y = 45
From the second part of the problem, Carlos purchased 3 additional dog leashes and 2 additional cat brushes for a total of $19. Thus, we can write the equation:
3x + 2y = 19
Now we have a system of equations:
6x + 6y = 45
3x + 2y = 19
We can solve this system by using the method of substitution or elimination. Let's use the method of elimination.
First, let's multiply the second equation by 2 to make the coefficients of 'y' in both equations the same:
6x + 6y = 45
6x + 4y = 38
Now, we can subtract the second equation from the first equation:
(6x + 6y) - (6x + 4y) = 45 - 38
This simplifies to:
2y = 7
Dividing both sides by 2, we find:
y = 7/2 or y = 3.5
Now, substitute this value of 'y' into one of the original equations to solve for 'x'. Let's use the first equation:
6x + 6(3.5) = 45
Simplifying:
6x + 21 = 45
Subtracting 21 from both sides:
6x = 24
Dividing both sides by 6, we find:
x = 4
So, the price of each dog leash is $4, and the price of each cat brush is $3.5.