Question

if x and y are non-negative integers and 3x + 4y = 96, how many pairs (x,y) are there?

Answer 1

Answer:

There are 9 pairs of (x, y) which meet the given conditions.

Step-by-step explanation:

3x + 4y = 96 . . . . . . . . . . . . . .  equation (i)

This a linear equation and represents a straight line on a two dimensional plain.

Putting y = 0, 3x = 96, x = 32.  ∴ The straight line meets X-Axis at (32, 0)

Putting x = 0, 4y = 96, y = 24.  ∴ The straight line meets Y-Axis at (0, 24)

Since, x and y are non-negative integers, pairs (x, y) are limited by these Points and can have integer values only.  Therefore, x co-ordinates can have values from 0 to 32, where corresponding y value is an integer.

(0, 24) is a solution

(4, 21) is next solution

(8, 18) is next solution

(12, 15) is next solution

(16, 12) is next solution

(20, 9) is next solution

(24, 6) is next solution

(28, 3) is next solution

(32, 0) is next solution.  

∴ There are 9 pairs (x, y) meeting given conditions.