If A+ B = 76
A-b = 38
A ÷ B =?

\( A+B=76\to A=76-B\\\\A-B=38\to A=38+B\\\\\Downarrow\\\\38+B=76-B\\B+B=76-38\\2B=38\ \ \ /:2\\B=19\\\\\Downarrow\\\\A=76-19=57 \)

\( \Downarrow\\\\A: B=57:19=3 \)

For this case we have the following system of equations:

\( A + B = 76\\A-B = 38 \)

Solving the system of equations we have:


1) We subtract equation 1 with equation 2:

\( 2B = 76 - 38\\2B = 38 \)


2) We clear the value of B:

\( B = \frac{38}{2}\\B = 19 \)


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

\( A-B = 38\\A-19 = 38\\A = 38 + 19\\A = 57 \)


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

\( \frac{A}{B}= \frac{57}{19} = 3 \)


Answer:

\( \frac{A}{B} = 3 \)


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