AMC 8 Daily Practice Round 8
Complete problem set with solutions and individual problem pages
In a kindergarten, there are three classes. Class has more students than Class , and Class has more students than Class . When distributing dates to the children: Each child in Class receives fewer dates than each child in Class ; each child in Class receives fewer dates than each child in Class . As a result: Class , in total, receives more dates than Class ; Class , in total, receives more dates than Class . How many dates were distributed to the three classes in total?
- A.
- B.
- C.
- D.
- E.
Let Class have children. From the given conditions:
Each child in Class receives fewer dates than each child in Class .
Thus, children in Class receive fewer dates than children in Class .
Since Class in total receives more dates than Class , and Class has more children than Class , these extra children together receive dates.
Therefore, each child in Class receives dates.
Similarly, children in Class receive fewer dates than children in Class .
Thus, each child in Class receives dates.
We then have the equation:
Solving gives .
Therefore:
Class has children, each receiving dates.
Class has children, each receiving dates.
Class has children, each receiving dates.
So, the total number of dates distributed is:
A total of dates were distributed to the three classes.
