Caitlin, Chris, and Molly are partners and share income and losses in a $3$:$4$:$3$ ratio $($in ratio form: Caitlin, $3/10$; Chris, $4/10$; Molly, $3/10).$ The partnership$$s capital balances are Caitlin, $$137,000$; Chris, $$97,000$; and Molly, $$117,000.$ Paul is admitted to the partnership on July $1$ with a $20\%$ equity and invests $$177,000.$ The balance in Caitlin$$s capital account immediately after Paul$$s admission is:

a

$$177,000$

b

$$158,420$

c

$$125,560$

d

$$138,420$

e

$$115,580$