Given
A positive integer is 48 more than 23 times another.
Their product is 12188.
To find the two integers.
Explanation:
Let x and y be the two positive integers.
Since a positive integer is 48 more than 23 times another.
Then,
[tex]y=23x+48\text{ \_\_\_\_\_\lparen1\rparen}[/tex]
Also, since their product is 12188.
Then,
[tex]\begin{gathered} xy=12188 \\ x(23x+48)=12188 \\ 23x^2+48x-12188=0 \\ 23x^2+554x-506x-12188=0 \\ x(23x+554)-22(23x+554)=0 \\ (23x+554)(x-22)=0 \\ x=22(\because x\text{ is a positive integer}) \end{gathered}[/tex]
That implies,
[tex]\begin{gathered} y=23x+48 \\ y=23\times22+48 \\ y=554 \end{gathered}[/tex]
Hence, the two integers are 22 and 554 respectively.
