#### Answer

One pair of dress socks costs 5.25

#### Work Step by Step

Let X represent the cost of a pair of athletic socks.
Dress socks cost 2.50 a pair more than athletic socks.
Thus, we obtain that if athletic socks cost X, dress socks cost X + 2.50.
Randall purchased one pair of dress socks and six pairs of athletic socks for 21.75.
One pair of dress socks means X + 2.50
And six pairs of athletic socks means + 6X
Thus, we obtain:
X + 2.50 + 6X = 21.75
7X + 2.50 = 21.75
Subtract 2.50 from both sides:
7X = 19.25
Divide both sides by 7:
X = 2.75
Since one pair of dress socks costs X + 2.50, and X = 2.75, one pair of dress socks costs 5.25.