a phrasal verb: work out

work, verb, /wɝk/

1) PLAN work something ↔ out    

to think carefully about how you are going to do something and plan a good way of doing it. 

to find or create (something, such as a solution or a plan) by thinking.

UN negotiators have worked out a set of compromise proposals.

work out what/where/how etc

We need to work out how we’re going to get there.

I had it all worked out (=had made very careful plans).

I'm trying to work out [=figure out] a way to do it.

We worked out a plan to save money.

We'll work the details out later.

I don't know how you're going to get there. You have to work that out for yourself.

2) CALCULATE work something ↔ out    

to calculate an answer, amount, price etc. 

to use mathematics to solve (something).

See if you can work this bill out.

work out how much/how many etc

We’ll have to work out how much food we’ll need for the party.

She worked out the problem on a piece of paper.

3) UNDERSTAND work something ↔ out (especially British English)    

to think about something and manage to understand it. 

to understand the behavior of (someone).

The plot is very complicated – it’ll take you a while to work it out.

work something out for yourself

I’m sure you can work it out for yourself.

He does these crazy things, and I just can't work him out. [=figure him out]

4) COST 

if a cost or amount works out at a particular figure, it is found to be that much when you calculate it.

work out at/to £10/$500 etc

The bill works out at £15 each.

work out expensive/cheap etc(=be expensive or cheap)

If we go by taxi, it’s going to work out very expensive.

It will work out (to be) cheaper [=it will be cheaper] if we take the bus instead of the train.

With tax, it worked out at/to just over $115. [=the total amount was just over $115]

5) GET BETTER 

if a problem or complicated situation works out, it gradually gets better or gets solved. 

to happen, develop, or end in a desired or successful way.

Things will work out, you’ll see.

I hope it all works out for Gina and Andy.

work itself out

I’m sure everything will work itself out.

Our plan worked out perfectly.

We broke up because things didn't work out between us.

6) HAPPEN 

if a situation works out in a particular way, it happens in that way SYN  turn out. 

to happen, develop, or end in a particular way or to have a particular result.

work out well/badly

Financially, things have worked out well for us.

Despite some difficulties, everything worked out well.

Things don't always work out the way you want them to.

I'm not sure how the story will work out.

How is your new roommate working out? [=how are things going with your new roommate?]

7) EXERCISE 

to make your body fit and strong by doing exercises. → workout. 

to perform athletic exercises in order to improve your health or physical fitness.

He works out with weights twice a week.

She works out at the gym twice a week.

8) I can’t work somebody out (British English, spoken)    

used to say that you cannot understand what someone is really like or why they behave in the way they do.

I couldn’t work her out at all.

He does these crazy things, and I just can't work him out. [=figure him out]

9) be worked out    

if a mine is worked out, all the coal, gold etc has been removed from it.