Need help with an SAT math problem?

<ol>
<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</p>

<p>I keep on getting C (30). I did C=2B. C-5=B+10. B=c/2. C-5=C/2 + 10. C/2=15 C=30.
but the answer keep on saying its 40 (E) which doesn't make any sense.</p>

<ol>
<li>If s equals (1/2) percent of t, what percent of s is t?</li>
</ol>

<p>A.) 2% B.) 200% C.) 2000% D.) 20,000% E.) 200,000%</p>

<p>Anyone know how to answer this type of question? (number 2).
Answers D.</p>

<p>Thanks!</p>

<ol>
<li> Let C = original number of books Carol has
Let B = original number of books Beverly has
Carol has twice as many books as Beverly has (C = 2B)
After Carol gives Beverly 5 books, she still has 10 more books than Beverly has (after Beverly gets 5 more books) (C-5 = 10 + (B+5))
Substitute C = 2B into the longer equation.
2B -5 = 10 + B + 5
B = 20 (Subtract B from both sides and add 5 to both sides)
C = 40 (substitution)</li>
</ol>

<p>To solve percent problems, you must understand the definition of percent and then translate the English words into proper equations.</p>

<p>a is b percent of c : a = b/100 * c
What percent of d is e? : e/d * 100 = ?</p>

<p>s equals (1/2) percent of t<br>
s = (1/2) /100 * t
So s = t / 200</p>

<p>What percent of s is t? Translated to math, we state:
t/s * 100 = ?
We then substitute s = t/200 into the above translation
t/s * 100 = t / (t/200) x 100 = 200 x 100 = 20000 %</p>

<p>If you don’t feel like doing algebra:</p>

<p>For the first one, just play with the answers. Say you try Carol has (c) = 30 books. Then Beverly has 15. If Carol gives Beverly 5, Carol will have 25 and Beverly will have 20. But that is not a difference of 10.</p>

<p>OK, try C = 40. then B = 20. Now take away 5 from C, add it to B: You get 35 and 25 which is a difference of 10. That’s it.</p>

<p>By the way, you were almost right with your algebra. You just forgot to increase B when you decreased C. But that’s the problem with algebra on the SAT – almost right is wrong.</p>

<p>For the second one, you could also make up numbers. Since S is 1/2 % of t, try letting t = 200, which will make s = 1 . Then you can see right away that t is 200 times bigger which is 20000%.</p>

<p>For students not strong in algebra I agree with Pc’s suggestion of plugging in the answer choices. I just want to add to that that I always start with choice (C) (as he has done) unless there is a specific reason not to.</p>