Answer :

[tex]A+B=76\to A=76-B\\\\A-B=38\to A=38+B\\\\\Downarrow\\\\38+B=76-B\\B+B=76-38\\2B=38\ \ \ /:2\\B=19\\\\\Downarrow\\\\A=76-19=57[/tex]

[tex]\Downarrow\\\\A:B=57:19=3[/tex]
carlosego

For this case we have the following system of equations:

[tex] A + B = 76

A-B = 38
[/tex]

Solving the system of equations we have:


1) We subtract equation 1 with equation 2:

[tex] 2B = 76 - 38

2B = 38
[/tex]


2) We clear the value of B:

[tex] B = \frac{38}{2}

B = 19
[/tex]


3) We substitute The value of B in equation 2 and obtain the value of A:

[tex] A-B = 38

A-19 = 38

A = 38 + 19

A = 57
[/tex]


Then, the value of the division of both numbers is:

[tex] \frac{A}{B}= \frac{57}{19} = 3
[/tex]


Answer:

[tex] \frac{A}{B} = 3 [/tex]