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Find the value of two integers if their sum is one hundred and seventy one and their difference is twenty-five.write the value of the greater integer

Sagot :

Let x be the greater integer

Let y be the smaller integer

their sum is one hundred and seventy one:

[tex]x+y=171[/tex]

their difference is twenty-five:

[tex]x-y=25[/tex]

Use the next system of equations:

[tex]\begin{gathered} x+y=171 \\ x-y=25 \end{gathered}[/tex]

1. Solve y in the second equation:

[tex]\begin{gathered} x-y=25 \\ -y=25-x \\ y=-25+x \end{gathered}[/tex]

2. Substitute the y in the first equation by th value you get in step 1:

[tex]x+(-25+x)=171[/tex]

3. Solve x:

[tex]\begin{gathered} x-25+x=171 \\ 2x-25=171 \\ 2x=171+25 \\ 2x=196 \\ x=\frac{196}{2} \\ \\ x=98 \end{gathered}[/tex]

Then, the greater integer is 98

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