With most 'brainteasers' in maths/physics most of it comes down to writing that first vital expression. Sometimes knowing what variables to make can be difficult - but hey practice makes perfect. In the first question think of what is changing, normally this indicates something that you should make a variable. Both Leah and Sue and John have ages, but we don't know what they are. Untill we find what they are they are free to change. Start with one of them. I choose Leah because she is mentioned first, but this will work with any of them.
Let Leah's age be x. Then Sue's age is 6 years less than Leah's, so instead of making a new variable, call her age x-6. Likewise for John's age x+5. The total of their ages is then.
T = x+x+5+x-6 = 3x - 1 = 41
3x = 42, x = 14
This was Leah's age. Sue is 6 years younger. Sue is 8.
The second one relies on ratio's - something that is often hard to get your head around. If the ratio is 3:2 then for every 5 parts of money there are we can split it up to Josh and Julie as 3 and 2 dollars respectively. Now we want to find how many '5$' are in $150 000
150 000 / 5 = 30 000 lots of $5
For every lot of $5 josh gets $3 -> josh gets 30 000 * $3 = $90 000
Julie gets $2 for every lot of $5 -> julie gets 30 000 * $2 = $60 000
as a final check $150 000 = $90 000 + $60 000
There isn't always an easy way to tell exactly what an equation will form, and the ratio example I gave wasn't the best becuase i didn't use variables. The first rule though is to try and use as few variables as possible. If you can express something in terms of something else, as in the case with the peoples ages, then generally you have a way of simplyfying the expression. As practice maybe you could try that question again but try and solve it with Sue's age as x and express the other peoples ages in terms of her's. Good luck with those brainteasers!