Question

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

Which is the value of x?

Answer 1

x =72

Explanation:

`(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:

`(75-y)/(y) =24`

`(75)/(y) -1 =24`

`(75)/(y) = 25`

`y=(75)/(25)`

y=3

so we have:

x=75-y

x=75-3

x=72

Answer 2

x=72

Explanation:

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

`(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:

`(x)/(75-x)=24`

Now

`x=24(75-x)\\ \\x=24\cdot 75-24x\\ \\x+24x=24\cdot 75\\ \\25x=24\cdot 75\\ \\x=(24\cdot 75)/(25)=24\cdot 3=72\\ \\y=75-72=3`