Final answer:
Mitochondria are the organelles that synthesize most of the ATP used by cells through the process of cellular respiration, especially when glucose and oxygen are available.
Step-by-step explanation:
The organelle that synthesizes most of the ATP used by cells when both glucose and oxygen are available is the mitochondria. These organelles are often referred to as the "powerhouses" or "energy factories" of the cell. Mitochondria are responsible for producing adenosine triphosphate (ATP), which is the cell's main energy-carrying molecule. This production of ATP through the process known as cellular respiration involves the breakdown of glucose and typically requires oxygen, consequently producing carbon dioxide as a waste product.
Cellular respiration occurs primarily within the mitochondria, where ATP is generated in large quantities. This is especially noticeable in cells with high energy demands, such as muscle cells. For example, the leg muscles of a marathon runner would contain high numbers of mitochondria to meet the energy requirements necessary for prolonged exercise.