# Thread: worded farction problem

1. ## worded farction problem

hi

pls can someone help with this question:

Mr Smith spent 1/3 of his salary on food and 2/5 of the remainder on transport.

what fraction of his salary has he left and also ifhe has £600 left find his salary

Hope you can help with this

thanks

2. Originally Posted by janvi anish
hi

pls can someone help with this question:

Mr Smith spent 1/3 of his salary on food and 2/5 of the remainder on transport.

what fraction of his salary has he left and also ifhe has £600 left find his salary

Hope you can help with this

thanks
The trick here is to see that the 2/5 spent on transport is of 2/3 the original amount.

Let his salary be $\displaystyle n$

Food: $\displaystyle \frac{n}{3}$

Transport: $\displaystyle \frac{2}{5} \times \frac{2}{3}n = \frac{4}{15}n$

Therefore his remaining salary is $\displaystyle \left[n(1- \left(\frac{2}{3}+\frac{4}{15}\right)\right] = \frac{n}{15}$

This value is equal to £600: $\displaystyle \frac{n}{15} = 600$

$\displaystyle n = 9000$ (and I'd love to be on that salary!)

3. hi
thks for this..but the answer says that he has 2/5 of his salary left and if he had £600 of his salary left then his salrary is 1500..i know that the answer might not always be right but thought this might help.....

4. Originally Posted by janvi anish
hi
thks for this..but the answer says that he has 2/5 of his salary left and if he had £600 of his salary left then his salrary is 1500..i know that the answer might not always be right but thought this might help.....
Nah, I'm probably wrong because 9000 is absurdly high anyway. This time I'll concentrate on what he has left

OK, let me try again.

After food he has 2/3 of his salary left.

After transport he has 3/5 of 2/3 of his salary left.

This means that overall he has $\displaystyle \frac{2}{3} \times \frac{3}{5} = \frac{2}{5}$ of his salary left (which is the first part answered)

If this is £600: $\displaystyle \frac{2}{5} \times 600 = 1500$

Sorry about that last post >.<

5. thanks very much for this....really appreciate it.....this was my 9 yr old sons h/wk and could not get my head round it!!!

6. Originally Posted by janvi anish
thanks very much for this....really appreciate it.....this was my 9 yr old sons h/wk and could not get my head round it!!!
No problem, it threw me initially too XD