The sum of two numbers is 580. the difference is 150. find the largest of the two numbers

X=small number
y=large number

x+y=580
y-x=150

y=580-x
(580-x)-x=150
-580          -580
-x-x=-430
-2x=-430
-2x/-2=-430/-2
x=215

215+y=580
-215     -215
y=365

FINAL ANSWER: The largest number is 365 and the small number is 215.

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.

The answer to the question is d