Help with Math question

Test Preparation SAT Preparation
1

<p>At Central High School each student studies exactly one foreign language. 3/5 of the students take Spanish, and 1/4 of the remaining students take Italian. if all of the others take French, what percent of the students take French?
A) 10
B) 15
C) 20
D) 25
E) 30</p>

<p>The book gives me the solution, but I want to know why the way I did it was wrong. </p>

<p>This is how I did it:
(3/5) times (1/4)= 3/20 so this is the fraction for the number of students taking Italian
Then, I found the common denominator for 3/5 and 3/20 which is 20
3/5= 12/20
Then: 12/20+3/20=15/20 to find the total number of students taking Spanish and Italian
20/20-15/20= 5/20 this is the fraction of the number of students taking French
Finally I simplified the fraction 5/20 and it gave me 1/4
1/4 is 25% so I thought that the answer was 25, but it's not.
The correct answer is 30. </p>

<p>Can someone please tell me why my method didn't lead me to the correct answer?</p>

<p>thanks a lot</p>

2

<p>This is what I did:</p>

<p>Start with 1. </p>

<p>Subtract 3/5, since the Spanish people can’t be doing French. </p>

<p>That leaves us with 2/5 of the students. </p>

<p>1/4 of this 2/5 is doing Italian, which means the other 3/4 must be doing French. </p>

<p>(2/5) * (3/4) = 3/10</p>

<p>Hope that helped!</p>

3

<p>The fraction of students taking Italian is 1/4 of 2/5, not 1/4 of 3/5. </p>

<p>3/5 of the students take Spanish. That’s 60%.
Of the remaining 40%, one fourth take Italian. That means 10% take Italian.
The other 30% take French.</p>

4

<p>Start with 100 students.</p>

<p>3/5 or 60 take Spanish. </p>

<p>1/4 of 40 take Italian, and that leaves you 30.</p>

5

<p>It’s nice to see you picking numbers for a change Xiggi. :)</p>

<p>I just want to emphasize that if you’re picking numbers in percent problems, always start with 100 as the total…the word percent means “out of 100” after all.</p>