Final answer:
The ripening of eggs within the ovarian follicles is primarily influenced by the Follicle-stimulating hormone (FSH), which is responsible for the development of ova, coupled with the Luteinizing hormone (LH), which promotes follicle maturation and ovulation.
Step-by-step explanation:
The hormone that influences the ripening of eggs within the ovarian follicles is the Follicle-stimulating hormone (FSH). FSH is responsible for the development of egg cells, or ova, within the structures known as follicles. Follicle cells also produce the hormone inhibin, which serves to inhibit FSH production.
The Luteinizing hormone (LH) also plays a critical role by stimulating the maturation of the growing follicles, inducing ovulation, and promoting the production of the hormones estradiol and progesterone. Both estradiol and progesterone are essential in preparing the body for pregnancy, with estradiol aiding in the development of secondary sex characteristics and both hormones regulating the menstrual cycle.