7x+3y=64
One number is 3 times the other number.
Let y=3*x representing 3 times the other number
y=3x
Substitute the y value in the equation
7x+3y=64
7x+3(3x)=64
7x+9x=64
16x=64
divide both sides by 16
x=4
Substitute the x value back in equation to solve for y
7x+3y=64
7(4)+3y=64
28+3y=64
Subtract 28 from both sides
3y=36
Divide both sides by 3
y=12
So x=4 and y=12 and the sister says one of the integers is 3 times the other. 4 goes into 12 by 3 times so these are your answers.
Hope this helped! :)