Melody

Sorry Alan,

I was working on it at the same time as you.

Patrick bought some dictionaries and files for $1 474.

The number of dictionaries he bought was 2/3 the number of files he bought.

The cost of a dictionary was $12 more than the cost of a file.

He spent $22 more on dictionaries than on files.

How much did a dictionary cost?     [Find n]

d dictionaries are bought for n  dollars each    So they will cost a total of   nd dollars

f files are bought for  m dollars   each                so they will cost a total of    mf   dollars

dn + fm = 1474

d= (2/3)f      and   n=m+12

substituting gives us

\(\frac{2}{3}*f (m+12)+fm=1474\\ \frac{2f}{3}*(m+12)+\frac{3fm}{3}=1474\\ 5fm+24f=1474*3\\ f(5m+24)=1474*3\qquad (1)\)

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

\(dn=fm+22\\ \frac{2f}{3}(m+12)=fm+22\\ 2fm+24f=3fm+66\\ 24f-fm=66\\ f(24-m)=66\qquad (2)\)

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

(1) divided by (2)

\(\frac{f(5m+24)}{f(24-m)}=\frac{3*1474}{66}\\ \frac{(5m+24)}{(24-m)}=67\\ 5m+24=67*24-67m\\ 72m=66*24\\ m=22\\~\\ n=22+12=34\)

the dictionaries cost   $34 each

Reposted here.

Here is the original

I have just realized that this is a repost.

Next time:

Please give the address of the original thread and ask someone (me if you want) to add to or comment on the original question.

Request them to also leave a note here to say they have done so.  

Thanks.

Guest just made a mistake calculating n.   The rest is right

This is an arithmetic progression.

The first number,  sometimes called 'a' or  T_1 is  1

d is the common difference,    4-1=7-4=....97-94 =  3

L is the last term = 97

You will need to find n (the number of terms) first

Use the formula 

\(T_n=a+(n-1)d\\ 97=1+(n-1)*3\)

you can finish solving that.

Then use the following formula to find the sum of all those n terms.

\(S_n=\frac{n}{2}[a+L]\)

There are a lot of formulas in the AP and GP topic.  You have to memorize them all.

I just looked and this question now has 2 answers.

Thanks  answerers.   

Next time could you please leave a note here saying that you have answered.  

Thanks for posting as I have requested. 

The only thing helperid is right about is that more words, especially polite words, would be more likely to give you the answer that you want.

Also, it is a little easier for answerers if you add the address with a hyperlink, but that is not a big deal.

Answerers,

Please answer on the original thread and leave a note here saying that you have done so.

4! = 24