Verified Answer :

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

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

carlosego

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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