Problem:
Four whole numbers, when added three at a time, give the sums 180,197,208 and 222. What is the largest of the four numbers?
Answer Choices:
A. 77
B. 83
C. 89
D. 95
E. cannot be determined from the given information
Solution:
Let the four numbers be w,x,y and z with w≤x≤y≤z. Since each number appears three times in the four sums,
3(w+x+y+z)=180+197+208+222=807.
Thus w+x+y+z=269 and w+x+y=180, so z=269−180=89.