The cost of four scarves and six hats is $52 the cost of two hats is a dollar more than the cost of one scarf what are the costs of one scarf and one hat
4 s + 6 h = 52
s + 1 = 2 h
substituting ... 4 s + 3 s + 3 = 52
... solve for s , then substitute back to find h
To find the cost of one scarf and one hat, let's assign variables to represent the unknowns:
- Let's say the cost of one scarf is "S" dollars.
- And let's say the cost of one hat is "H" dollars.
From the given information, we can establish two equations:
1) The cost of four scarves and six hats is $52:
4S + 6H = 52
2) The cost of two hats is a dollar more than the cost of one scarf:
2H = S + 1
Now we can solve these two equations simultaneously to find the values of S and H.
Let's rearrange equation 2) to make it easier to use in equation 1):
2H - S = 1
Now, we can use either substitution or elimination method to solve these equations. Let's use substitution:
From equation 2), we can express S in terms of H:
S = 2H - 1
Substitute this value for S in equation 1):
4(2H - 1) + 6H = 52
Now, solve for H:
8H - 4 + 6H = 52
14H = 56
H = 4
Now substitute the value of H back into equation 2) to find S:
2(4) = S + 1
8 = S + 1
S = 7
Therefore, the cost of one scarf is $7, and the cost of one hat is $4.