Let's use n to represent an integer (whole number). Since we need three integers, let's define them like this:
color(blue)(n)=1st integer
color(red)(n+1)=2nd integer
color(green)(n+2)=3rd integer
We know we can define the second and third integers as n+1 and n+2 due to the problem telling us that the integers are consecutive (in order)
Now we can make our equation since we know what it's going to equal:
color(blue)(n)+color(red)(n+1)+color(green)(n+2)=48
Now that we've set up the equation, we can solve by combining like terms:
3n+3=48
3n=45 color(blue)(" ""Subtract " 3 " from both sides")
n=15 color(blue)(" "45/3=15)
Now that we know what n is, we can plug it back into our original definitions:
color(blue)(n)=15 color(blue)(" 1st Integer")
color(red)(15+1)=16 color(red)(" 2nd Integer")
color(green)(15+2)=17 color(green)(" 3rd Integer")
color(blue)(15)+color(red)(16)+color(green)(17)=48 " True"
