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To find the number of cups of onion needed, we need to determine the fraction of the extended ratio that corresponds to onion.
The extended ratio 1:3:9 tells us that there is 1 part of green pepper, 3 parts of onion, and 9 parts of tomato.
To find the total number of parts in the extended ratio, we add the parts together: 1 + 3 + 9 = 13 parts.
To find the fraction of the extended ratio that corresponds to onion, we divide the number of parts of onion (3) by the total number of parts (13): 3/13.
Finally, we multiply the fraction of the extended ratio that corresponds to onion by the total amount of salsa needed (117 cups): (3/13) * 117 = 27 cups of onion.
Therefore, we need 27 cups of onion to make 117 cups of salsa.