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?
A ) $4.00
B ) $5.00
C ) $6.00
D ) $7.00
Let's denote the cost of one scarf as S and the cost of one hat as H.
From the problem, we have two equations:
1) The cost of four scarves and six hats is $52.00
4S + 6H = $52.00 ...(1)
2) The cost of two hats is $1.00 more than the cost of one scarf
2H = S + $1.00 ...(2)
We need to find the value of S (the cost of one scarf).
Let's solve equation (2) for H:
2H = S + $1.00
H = (S + $1.00)/2 ...(3)
Now let's substitute equation (3) into equation (1):
4S + 6*( (S + $1.00)/2 ) = $52.00
4S + 3*(S + $1.00) = $52.00
4S + 3S + $3.00 = $52.00
7S + $3.00 = $52.00
Now let's solve for S:
7S = $52.00 - $3.00
7S = $49.00
S = $49.00 / 7
S = $7.00
Therefore, the cost of one scarf is $7.00.
The correct answer is D) $7.00.