The cost of four scarves and six hats is $52.00. The cost of two hats is $1.00 more than the cost of one scarf. What is the cost of one scarf? (1 point) Responses $4.00 $4.00 $5.00 $5.00 $6.00 $6.00 $7.00 $7.00

Question

The cost of four scarves and six hats is $52.00. The cost of two hats is $1.00 more than the cost of one scarf. What is the cost of one scarf? (1 point) Responses $4.00 $4.00 $5.00 $5.00 $6.00 $6.00 $7.00 $7.00

Answer 1

Let x be the cost of one scarf.

The cost of two hats is x + $1.00.
The cost of four scarves is 4x.
So, the cost of four scarves and six hats is 4x + 6 * (x + $1.00) = $52.00
Simplifying the expression, we get 4x + 6x + $6.00 = $52.00
Combining like terms, we get 10x + $6.00 = $52.00
Subtracting $6.00 from both sides of the equation, we get 10x = $46.00
Dividing both sides of the equation by 10, we get x = $4.60
Therefore, the cost of one scarf is $4.00. Answer: \boxed{4}.

Answer 2

Let's assign variables to the cost of one scarf and one hat. Let x be the cost of one scarf and y be the cost of one hat.

According to the given information, the cost of four scarves and six hats is $52.00, so we can write the equation:

4x + 6y = 52

The cost of two hats is $1.00 more than the cost of one scarf, which can be expressed as:

2y = x + 1

Now we can solve these equations to find the cost of one scarf.

From the second equation, we can express x in terms of y:

x = 2y - 1

Substituting this value of x into the first equation:

4(2y - 1) + 6y = 52

8y - 4 + 6y = 52

14y - 4 = 52

14y = 56

y = 56/14

y = 4

Now we can substitute the value of y back into the equation x = 2y - 1 to find the cost of one scarf:

x = 2(4) - 1

x = 8 - 1

x = 7

So, the cost of one scarf is $7.00.

Answer 3

To find the cost of one scarf, let's set up some equations based on the given information:

Let's assume that the cost of one scarf is "x" dollars.
According to the second piece of information, the cost of two hats is $1.00 more than the cost of one scarf, which translates to "2(x) = x + $1.00."
Simplifying this equation, we get 2x = x + $1.00.

Now, let's use the first piece of information to set up another equation:
The cost of four scarves and six hats is $52.00, which can be written as "4(x) + 6(y) = $52.00," where "y" represents the cost of one hat.

Simplifying this equation, we get 4x + 6y = $52.00.

Now we have a system of two equations:
2x = x + $1.00 (equation 1)
4x + 6y = $52.00 (equation 2)

To find the cost of one scarf (x), we need to solve this system of equations.

We can start by subtracting x from both sides of equation 1:
2x - x = x + $1.00 - x
x = $1.00

Therefore, the cost of one scarf is $1.00.

So, the correct answer is $1.00.