The headline of Floyd Mayweather tipped waitress $10,000 to help change her life - but wanted nobody to know . says:

1) Floyd Mayweather’s secret $10,000 tip to help waitress change her life.

a) Is the underlined portion above equivalent to the following?

Floyd Mayweather’s secret $10,000 tip in order to help waitress change her life.

where the underlined part is modifying the noun "tip" adjectivally.

b) Can sentence (1) be written like this as well?

Floyd Mayweather’s secret $10,000 tip for helping waitress change her life.

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