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Thanks for your question - I am Sam and I am one of the UK tax experts here on Just Answer.
The first job 29 hours at £9 an hour will be £261 a week from which tax will be charged on the amount over and above £211.54 (so approx £9.89 and also National Insurance as the first £112 is National Insurance free so the balance is liable meaning a deduction of approx £12.82 so total deductions £22.71 leaving a net payment of £238.29
Then the second job will be taxed BR (20%) so 6 hours x £8.50 = £51 x 20% for tax = £10.20 and no National Insurance as below the limit (for tax purposes income is added together and one tax free element allocated, whereas each source of income for National Insurance considers the free element)
So she should take home approx £40.80
This is based on the fact that this are her sole incomes
Let me know if I can assist further