19. Sacha places 25 counters into 14 boxes so that each box contains 1,2 or 3 counters. No box is inside any other box. Seven boxes contain 1 counter. How many contain 3 counters?
A 2
B 3
C 4
D 5
E 6
Solution
C

Since seven boxes contain one counter, the remaining seven boxes contain 18 counters. Let the number of boxes containing 3 counters be $x$. Therefore $3 x+2(7-x)=18$. Hence $3 x+14-2 x=18$ which has solution $x=4$. Therefore four boxes contain 3 counters.