Question

If $4x+3y=120$, find how many non-negative integer solutions are possible?

• A. $1$
• B. $11$
• C. Infinite
• D. None of these

Answer 1

The correct option is D None of these

We can write the equation in another form $4(x-3)+3(y+4)=120$
Now, we make a table

x	30	27	24	21	18	15	12	9	6	3	0
y	0	4	8	12	16	20	24	28	32	36	40

We observe a patter that $x$ reduces by $3$ and $y$ increases by $4$. But both $x$ and $y$ cannot be negative or $0$. So, the value of $x=0$ and $y=0$ is ruled out. Hence, nine such positive integer solutions are possible.
Alternately, we can write the given equation as $4(x+3)+3(y-4)=120$. We get the same values of $x$ and $y$