Fran Massey earns three times as much as an actuary then she does as a writer. her total income is $40000 more than that of her brother who earns only half as much as Fran does an actuary. What is Frans salary as an actuary?

Question

anonymous · Answer

lets say for example that her income was $$36,000$ 
how much did she make as an actuary, and how much did she make as a writer?

anonymous · Answer

if it is not clear, let me know and i will see if i can explain it

anonymous · Answer

she made 12,00 as a writer i believe

anonymous · Answer

not quite
i think you divide by 3 but 

if she made $12,000 as a writer, and made three times as much as an actuary, then she made $3\times 12000=36000$ as an actuary for a total of $12,000+36,000=48,000$ so that is not right

anonymous · Answer

the correct answer is $9,000$ because if you multiply that by 3 you get $27,000$  for a total of $36,000$

anonymous · Answer

in other words, this line
Fran Massey earns three times as much as an actuary then she does as a writer.
can be interpreted this way:
if she makes $x$ amount as a writer, then she makes $3x$ as an actuary for a total of $4x$

anonymous · Answer

her brother makes half as much as she does as an actuary
if she makes $3x$ as an actuary, then her brother makes $\frac{3}{2}x$ total

anonymous · Answer

ok that was wrong, sorry
if she make $40,000$ more than her brother, we can set 
$$4x=\frac{3}{2}x+40,000$$ and solve for $x$

anonymous · Answer

do you know how to solve this?  it takes two steps

anonymous · Answer

yes

anonymous · Answer

let me know what you get
then we can finish the problem

anonymous · Answer

16000

anonymous · Answer

k good
then that is the amount she makes as a writer, she makes 3 times that much as an actuary which is what you are asked for

anonymous · Answer

so she makes 40000

anonymous · Answer

no she makes $16,000$  as a writer and so $3\times 16,000$ as an actuary

anonymous · Answer

i get $$48,000$ as an actuary

anonymous · Answer

this was kind of a complicated word problem
there are probably other ways to solve, but i don't think any are easier

anonymous · Answer

yeah i got 48000 when i checked it again

anonymous · Answer

oh good

anonymous · Answer

alright well thank you for your help