Expressing Unknowns Using a Known Total
When the total number of items in a collection is known and the items come in exactly two types, the count of the second type can be found by subtracting the count of the first type from the total. If the total is a specific number and one type is represented by , the other type is represented by .
For example, suppose a seller sold a total of tickets, each being either an adult ticket or a child ticket. If the number of child tickets sold is known, the number of adult tickets is found by subtracting from :
| Child tickets | Adult tickets |
|---|---|
| 20 | 80 |
| 45 | 55 |
| 75 | 25 |
In each row, the same reasoning applies: subtract the number of child tickets from to get the number of adult tickets. Generalizing with a variable, if child tickets were sold, then adult tickets were sold.
This approach differs from situations where one quantity is described relative to the other (such as "five more than" or "three times as many"). Here, both quantities are linked through a known total rather than through a direct comparison between the two unknowns, and the subtraction expression captures that relationship.
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