Answer:
x=72
Step-by-step explanation:
"An integer x is divided by an integer y, and the quotient is 24" mathematically sounds as
[tex]\dfrac{x}{y}=24[/tex]
"The sum of these two integers is 75" has the equation
[tex]x+y=75[/tex]
From the second equation
[tex]y=75-x[/tex]
Substitute it into the first:
[tex]\dfrac{x}{75-x}=24[/tex]
Now
[tex]x=24(75-x)\\ \\x=24\cdot 75-24x\\ \\x+24x=24\cdot 75\\ \\25x=24\cdot 75\\ \\x=\dfrac{24\cdot 75}{25}=24\cdot 3=72\\ \\y=75-72=3[/tex]
