Melody

Geno is right     but it is undefined.  YOU CANNOT divide by 0.   NOT EVER!

High Sweaty,

Start by multiplying both sides by 3  Then see if you can do it.  

Let me know how you get on :)

Anything divided by 1 stays the same so

X=890/450 = 89/45 = 1 and 44/45

67.4 and 34.4

do

674/344 = $${\frac{{\mathtt{674}}}{{\mathtt{344}}}} = {\frac{{\mathtt{337}}}{{\mathtt{172}}}} = {\mathtt{1.959\: \!302\: \!325\: \!581\: \!395\: \!3}}$$

the ratio is        337:172

@@ End of Day Wrap   Sun 2/8/15     Sydney, Australia Time   11:05pm  ♪ ♫

Hi everyone,

It has been quiet and I don't suppose there are not too many people about to notice that this wrap has even be written but there have been some great answers from CPhill, Nauseated, Radix and Heureka and I do want to thank you.  

I am told that the U.S. students are starting back at school after their summer break so the forum should be getting busier soon.  Too bad I like it quiet but even I know there are some distict advantages when it is busier.  The social posts are better just for starters. :)  TitianiumRome has had to hold up the social posting almost entirely by himself and a great job you have done of it too TR.  

ok Nauseated you have a lot of figures there but I am going to be so bold as to summarize your reasoning.

The question does not state WHEN the money was deposited into the account.

IF it is deposited at the very beginning of the month then it is an annuitiy due question and yours and Alan figures are correct (a tiny bit too big)

If it is deposited at the very end of the month then it is an ordinary annuity question and my original answer was in fact correct. (a tiny bit to small)

HOWEVER

If the $200 deposit is made at another time or times during the month then this will make the Future value lie between  the 2 extremes.

SEE Nauseated - that was not so hard.  You really did not need all those tables of values.

I am quite positive you will correct me if I have misinterpreted your logic.

-----------------------------------

The reason I have added "a tiny bit too big" and a "tiny bit too small" is because there is always going to be one day at the end, or the beginning, of the month which has the old value at the beginning and the new value at the end so effectively this day has interest paid on the new deposit of only $100  (average of 0 and 200) [Not 0 (ordinary annuity) or 200 (annuity due)  as used for the development of the formula]

change   220.59 base 10 to base 8

Mmm, the whole number part is easy enough

220/8 = 27 remainder 4

27/8=3 remainder 3

3/8=0 remainder 3

so     $$220_{10}=334_8$$

Now the decimal part - I have never done this before.

There is no power of 8 that is also a power of 10 so it will have to be an approximation.

I will work it out to 3 base 8  places and then round it back to 2 I think.

$$\\\frac{59}{10^2}=\frac{x}{8^3}\\\\
59*8^3/100 = 302.08\\\\
so\;\;\;\; X\approx 302\\\\
\frac{59}{10^2}\approx \frac{302}{8^3}\\\\
$now change $302_{10}$ to base 8$\\\\$$

302/8=37 remainder 6

37/8=4 remainder 5

4/8= 0 remainder 4

so

$$\\302_{10}=456_{8}\\\\
so\\\\
0.59 \;(base10)\approx 0.456\; (Base8) \approx 0.46 \;\;$to 2 base 8 places$$$

SO 

$$220.59_{10}\approx 334.46_{8}$$

I just checked it with Wolfram alpha and it is correct  

I got 216.

Thanks Chris,  you are right, this question can be tackled very easily your way :)

This is a fairly simple example and it can be worked out just as CPhill says and it is easier that way too. :)