<p>Hey guys,</p>
<p>I am having trouble figuring out how to get the solution to two math problems:</p>
<li>Carol has twice as many books as Beverly has. After Carol gives Beverly 5 books, she still has 10 more books than Beverly has. How many books did carol have originally?</li>
</ol>
<p>a. 20 b. 25 c 30 d 35 e 40
I tried solving algebraically but couldn’t figure out</p>
<li>If s equals 1/2 percent of t, what percent of s is t?</li>
</ol>
<p>a. 2% b. 200% c. 2,000% d. 20,000% e. 200,000%</p>
<p>Could you please explain how you came up with the answers?
Thanks!</p>
<p>well, for #1
i did the following....first of all eliminated answers b and d since u cant have 17.5 or 12.5 books....</p>
<p>alright, for the algebra, it would have taken me longer, so i started doing them as plug ins....in this case the answer is E.40</p>
<p>u see, half of 40 is 20, then carol gives beverly 5 books, so she has 35, and now beverly has 25, which is 10 more books as stated in the problem.</p>
<p>for #2....</p>
<p>i just assigned random values....</p>
<p>s=.05 and t is 1, so then u just put t over s and get 20, which means its 20 times greater but really is 2000 percent.</p>
<p>answer to #1 is E</p>
<p>Carol has 40 books, Bev has 20 books
Carol gives B 5 books (she has 35 left), (Bev now has 25 books)</p>
<p>lets say S=5, T= 100</p>
<p>100/5 is 20
it asks for % so you multiply 20 x 100.</p>
<p>C is the answer</p>
<p>thanks BigWeight and anhtimmy. I quite didn't understand why T is being divided by S. </p>
<p>Is this the case?</p>
<p>s = .05T</p>
<p>what percent of S is T</p>
<p>what =? <- this is what you are finding.
perfect =%
S=S
T=T</p>
<p>so plug in, ?% x S=T</p>
<p>now rearrange it.
so %=(T/S) x 100</p>
<p>remember to get % you must multiply 100.</p>
<p>OH!!!! now I get it! thanks anhtimmy</p>
<p>no problem. :]
% problems may be confusing but just remember what each word represents and you'll be fine.</p>
<p>hey anhtimmy,</p>
<p>I just check the answer and it was d. 20,000%</p>
<p>i found what i did wrong.
.5% of 100 isn't 5, its .5 lol!</p>
<p>%=(T/S) x 100
(100/.5) x 100 = 20,000</p>
<p>my apologies. >.<</p>
<p>using algebra to solve #1</p>
<p>c = carol
b = Beverly </p>
<p>c = 2b (Carol has twice as many books as Beverly)</p>
<p>therefore b = c/2</p>
<p>c = 2b - 5 (Carol gives Beverly 5 books)</p>
<p>(Beverly gets 5 books from Carol) b + 5 ==> c/2 + 5 = (c + 10)/2 </p>
<p>so now b = (c + 10)/2 and c = 2b - 5</p>
<p>(c + 10)/2 + 10 = c (Carol still has 10 more books than Beverly) </p>
<p>(c + 10)/2 + 10 = 2b - 5</p>
<p>Now substitute (remember b = c/2)</p>
<p>(c + 10)/2 + 10 = 2(c/2) - 5
(c + 10)/2 + 10 = c - 5
(c + 10 + 20)/2 = c - 5
c + 10 + 20 = 2(c - 5)
c + 30 = 2c - 10
30 + 10 = 2c - c
c = 40</p>
<p>Or, if you want a slightly easier method.</p>
<p>c = 2b
c - 5 = b + 5 + 10 ==> c = b + 20</p>
<p>Plugging in 2b for c in the second equation yields:</p>
<p>2b = b + 20 ==> b = 20
c = 2b ==> c = 40</p>