His toolbox, as well as others, was put in its place.

This sentence contains a dependent clause set off by commas (“as well as others”). Because that information is not critical to the sentence, you can ignore those words and focus on the toolbox — a singular noun. 

Someone on the crew left his or her flashlight behind.

“Someone,” “everyone,” and “no one” are always singular. An easy way to remember this rule is to notice the word “one” in each word or term: Someone, everyone, and no one. 

In this example, we have three singular pronouns to choose from: “its,” “his,” or “her.” Because the sentence is referring to a person on the crew rather than the crew as a unit, we can eliminate “its.” That leaves us with “his” or “her.” The sentence does not tell us the gender of the crew member, so we must use “his or her.”

Everyone at the meeting voted to volunteer his or her time for charity.

“Someone,” “everyone,” and “no one” are always singular. In this example, the subjects are people. So, we must choose singular pronouns that apply to people rather than things. Our choices are “his” or “her.” The sentence does not indicate that the meeting was attended by members of only one gender, so we must use “his or her.”

One of our suppliers would like the CEO to reconsider its bid.

 “One” is singular, so it requires a singular pronoun. Furthermore, “supplier” is singular (“its”) because companies, agencies, and other organizations are always singular.

The members of the project team have received their assignments.

In this example, the sentence is describing the members of the team as individuals in a group (plural) rather than the team as a unit (singular). So, the pronoun must be plural.

Neither their supervisor nor the welders bought their supplies.

In this example, there are two nouns: “their supervisor,” which is singular, and “the welders,” which is plural. Because the word “nor” splits the two nouns so that they stand alone instead of together, focus on the closest noun. In this case, the closest noun is “the welders,” so use the plural pronoun “their.”

Either Maureen or the marketing team will present its ideas for the grand opening.

Because the word “or” splits the two nouns so that they stand alone instead of together, focus on the closest noun. In this case, the closest noun is “the marketing team.” The team is one unit, so it is singular.

Either the students or Sarah will get her way regarding the dress code.

Because the word “or” splits the two nouns so that they stand alone instead of together, focus on the closest noun. In this case, the closest noun is “Sarah.”

Each of the companies posted its ad on the website.

 “Each” and “every” are singular because they focus on the individual parts of a collection or group rather than on the group as a whole.