Question

If 5 x + 12 Y = 80 find x, y integers (+ve) satisfying the equation.

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Answer 1

Step-by-step explanation:

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Answer 2

The positive integers x, y satisfying the equation 5x + 12y = 80 is x = 4, y = 5

Step-by-step explanation:

Given

$5x+12y=80$

$\implies 5x=80-12y$

$\implies x=\frac{80-12y}{5}$

$\implies x=16-\frac{12y}{5}$

Given that x and y should be positive integers

Therefore,

$12y/5$ should be an integer and its value should be less than 16

This means that y must be a multiple of 5 (i.e. 5, 10, 15, ...)

Thus,

If $y=5$

Then $x=16-\frac{12\times 5}{5}$

$\implies x=16-12$

$\implies x=4$

If $y=10$

Then $x=16-\frac{12\times 10}{5}$

$\implies x=16-24$

$\implies x=-8$

Therefore, the only set of positive integers that satisfies the equation is $x=4, y=5$

Hope this answer is helpful.

Know More:

Q: x, y are natural numbers such that x > y. Also x + y + xy = 80, then value of x is :

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