So,
We can "translate" these statements into mathematical open phrases.
"The sum of two numbers is 580."
x + y = 580
"The difference is 150."
x - y = 150
So we have our two equations:
x + y = 580
x - y = 150
It is easy to see that we can use Elimination by Addition by adding the two equations together and solving for x.
2x = 730
Divide both sides by 2.
x = 365
Substitute 365 for x in the first equation.
365 + y = 580
Subtract 365 from both sides.
y = 215
Check.
365 + 215 = 580
580 = 580
365 - 215 = 150
150 = 150
So the larger number is 365 and the smaller number is 215. We are interested in the larger number, so the answer is 365.
