Math Question........

The cost of four scarves and six hats is $52.00. The cost of twho hats is $1.00 more than the cost of one scarf.
a.What is a system of equations to represent the soulution?


b.What is the cost of one scarf?

c.What is the cost of one hat?

four scarves and six hats is $52.00
4s+6h=52

two hats is $1.00 more than the cost of one scarf.
2h=1s+1
2h=s+1
s=2h-1

substitute for s
4s+6h=52
4(2h-1)+6h=52
8h-4+6h=52
14h=56
h=4

s=2h-1
s=8-1
s=7

a scarf cost $7
a hat cost $4

4s + 6h = 52
2h = s + 1 or s = 2h - 1
substitute the second equation into the first equation:
4(2h - 1) + 6h = 52
8h - 4 + 6h = 52
14h = 56
h = 56/14 = 4
using the second equation:
s = 2(4) - 1 = 7
check using the first equation:
4(7) + 6(4) = 52
28 + 24 = 52
52 = 52
One scarf costs $7, one hat costs $4.

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4S + 6H = 52
2H = S + 1

4S + 3(S+1) = 52
4S + 3S + 3 = 52
7S = 49
S = 7

2H = 7 + 1
2H = 8
H = 4