let x = the larger number
let y = the smaller number
we can set up a system of equations with this:
x+y=77.95
x-y=30.61
take the second equation:
x-y=30.61
add y to both sides, cancelling it out on the left, and you get:
x=y+30.61
Now, since we know what x equals(not the exact number, though), we can plug it into the first equation so we can solve for y
We take the first equation now:
x+y=77.95
substitute x's value into the equation:
(y+30.61)+y=77.95
then, using the commutative and the associative property of addition, we can switch the order and parentheses around:
(y+y)+30.61=77.95
y+y=2y, so we can simplify the equation to:
2y+30.61=77.95
we subtract 30.61 from both sides:
2y=47.34
divide both sides by 2 to get your smaller number, y:
y=23.67
We can substitute y into the second equation now:
x-y=30.61
x-23.67=30.61
add 23.67 to both sides to get:
x=54.28
So the 2 numbers are 54.28 and 23.67