Problem:
The sum of three numbers is . The first is times the sum of the other two. The second is seven times the third. What is the product of all three?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let , and be the three numbers. Replace by four times the sum of the other two to get
Then replace with to get
The other two numbers are and , and the product of the three is .
Let the first, second, and third numbers be , and , respectively. Then so and the product is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions