Question

If $x$ and $y$ are $+$ve integers, then find the solution of the following equation:

$7x+12y=220$

• A. $(28,2)$
• B. $(16,9)$
• C. $(4,16)$
• D. $(12,10)$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $(28,2)$
B $(16,9)$
C $(4,16)$

Write the equation in the form of $x$ and $y$

$x=\frac{1}{7}(220-12y)$ or $y=\frac{1}{12}(220-7x)$

Now give +ve integral values to y such that x also becomes +ve integral. The first +ve integral value of y is 2(as y=1 will not make x, +ve and integral) so that

$x=\frac{1}{7}(220-24)=\frac{196}{7}=28.$

$\therefore x=28,y=2$

We choose only x=16 and 4, which are +ive such that y also becomes +ve integral.

For $x=16$,

$y=\frac{1}{12}(220-7\times 16)$

$\therefore 12y=220-112=108,\therefore y=9.$

For $x=4$,

$y=\frac{1}{12}(220-7\times 4)$

$12y=220-28=192,\therefore y=16$.

Hence $(x,y)=(28,2),(16,9),(4,16)$ only.