Question

An integer x is divided by an integer y, and the quotient is 24. The sum of these two integers is 75.

Answer 1

Answer:

x =72

Step-by-step explanation:

$\frac{x}{y} = 24$   equation 1

x+y=75   equation 2

using equation 2 we have:

x=75-y  equation 3

using equation 3 in equation 1 we have:

$\frac{75-y}{y} =24$

$\frac{75}{y} -1 =24$

$\frac{75}{y} = 25$

$y=\frac{75}{25}$

y=3

so we have:

x=75-y

x=75-3

x=72

Answer 2

Answer:

x=72

Step-by-step explanation:

"An integer x is divided by an integer y, and the quotient is 24" mathematically sounds as

$\dfrac{x}{y}=24$

"The sum of these two integers is 75" has the equation

$x+y=75$

From the second equation

$y=75-x$

Substitute it into the first:

$\dfrac{x}{75-x}=24$

Now

$x=24(75-x)\\ \\x=24\cdot 75-24x\\ \\x+24x=24\cdot 75\\ \\25x=24\cdot 75\\ \\x=\dfrac{24\cdot 75}{25}=24\cdot 3=72\\ \\y=75-72=3$