Answer:
19 and 13
Step-by-step explanation:
Let x be the larger number and y the smaller , then
[tex]\frac{3x}{y}[/tex] = 4 + [tex]\frac{5}{y}[/tex] ( multiply through by y to clear the fractions )
3x = 4y + 5 ( subtract 4y from both sides )
3x - 4y = 5 → (1)
and
[tex]\frac{6y}{x}[/tex] = 4 + [tex]\frac{2}{x}[/tex] ( multiply through by x to clear the fractions )
6y = 4x + 2 ( subtract 4x from both sides )
- 4x + 6y = 2 → (2)
Multiplying (1) by 4 and (2) by 3 and adding will eliminate x
12x - 16y = 20 → (3)
- 12x + 18y = 6 → (4)
Add (3) and (4) term by term to eliminate x
0 + 2y = 26
2y = 26 ( divide both sides by 2 )
y = 13
Substitute y = 13 into (1) and solve for x
3x - 4(13) = 5
3x - 52 = 5 ( add 52 to both sides )
3x = 57 ( divide both sides by 3 )
x = 19
The 2 numbers are 19 and 13
