Answer with Step-by-step explanation:
Let s represents the cost of scarfs
and h represents the cost of hats.
Cost of four scarfs and six hats is $52.00
i.e. 4s+6h=52
Cost of two hats is $1.00 more than the cost of one scarf.
i.e. 2h=s+1
s=2h-1
substituting s in 4s+6h=52
4(2h-1)+6h=52
8h-4+6h=52
14h=56
h=4
s=2h-1
s=8-1
s=7
Hence,
Cost of one scarf= $7
and Cost of one hat= $4
To solve the problem we need to make two expressions of the statements given to us.
The cost of 1 scarf is $7, and the cost of 1 hat is $4.
Given to us
Assumption
Let the cost of a scarf be x and the cost of a hat be y.
The cost of four scarves and six hats is $52.
4x + 6y = $52,
The cost of two hats is $1 more than the cost of one scarf.
2y = $1 + 1x
solving the expression for y,
[tex]2y = \$1 + 1x\\y = \dfrac{1 + 1x}{2}[/tex]
Substitute the value of y in expression 1
[tex]4x + 6y = $52\\\\ 4x + 6(\dfrac{1 + 1x}{2}) =52\\\\4x + 3(1 + 1x) = 52\\4x + 3 +3x = 52\\\\7x = 52-3\\\\x = \dfrac{49}{7}\\\\x = 7[/tex]
Substitute the value of x, in the expression of y,
[tex]y = \dfrac{1 + 1x}{2}\\\\y = \dfrac{1 + 7}{2}\\\\y = \dfrac{8}{2}\\\\y = 4[/tex]
Hence, the cost of 1 scarf is $7, and the cost of 1 hat is $4.
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