Question

How many solutions are there for the equation A+B+3C = 10 if A,B,C are whole numbers?

• A. 22
• B. 25
• C. 24
• D. 14

Answer 1

The correct option is B

25

It is given that A,B and C can take values ≥0
Give values to C from 0 to 3
At C=0, the equation changes to A+B=10. Number of solutions will be based on arrangement of 10 zeroes and 1 one = ${}^{11}$C${}_1$= 11
At C=1, the equation changes to A+B=7. Number of solutions=${}^8$C${}_1$=8
At C=2, the equation changes to A+B=4. Number of solutions=${}^5$C${}_1$=5
At C=3, the equation changes to A+B=1. Number of solutions=${}^2$C${}_1$=1

Total number of solutions = 11+8+5+1 = 25