<p>each student in a group of 30 studies german, italian, or both. The total number of students studying german is three more than the total number of students studying Italian. If the number of students that study both subjects is the same as the number of students that study exactly one subject, how many students in the group study only italian.</p>
<p>oh answer choices are </p>
<ol>
<li>6</li>
<li>9</li>
<li>15</li>
<li>21</li>
<li>24</li>
</ol>
<p>g=l+3</p>
<p>15 study both
15 only one</p>
<p>that means there’s a minimum of 15 for italian</p>
<p>you can eliminate 4 and 5 because a maximum of 15 combined study only one</p>
<p>so since there share a common minimum value of 15, for g to maintain an advantage of 3, 3 more students has to take it only than italian only, and the two have to add up to 15</p>
<p>the only choice that has a chance of doing that is 6</p>
<p>but if that’s not clear enough</p>
<p>eliminate 3, if 15 take both and 15 only italian, then 30 take italian and 15 german; impossible</p>
<p>test 9</p>
<p>9 only italian, 6 only german, resulting in 3 more taking italian than german–impossible
leaving only 6</p>
<p>g+i+b = 30
g=3+i
g+i = b</p>
<p>3+2i=b</p>
<p>3+i+i+3+2i = 30
4i+6 = 30
4i = 24
i = 6</p>
<p>each student in a group of 30 studies german, italian, or both. The total number of students studying german is three more than the total number of students studying Italian. If the number of students that study both subjects is the same as the number of students that study exactly one subject, how many students in the group study only italian.</p>
<p>30 Total
3+I=G
15 study both</p>
<p>( 9 ( 15 ) 6 )</p>
<p>6 only Italian</p>
<p>Let ‘G’ stand for those studying German,
‘I’ for those studying Italian,
and ‘B’ for those studying both</p>
<p>So,</p>
<p>G + I + B = 30</p>
<p>If The total number of students studying German is three more than the total number of students studying Italian, then:</p>
<p>G = I + 3</p>
<p>So, now the equation looks like this:</p>
<p>(I+3) + I + B = 30</p>
<p>If If the number of students that study both subjects is the same as the number of students that study exactly one subject, then</p>
<p>B = I + G and since we already figured out ‘G’ is I + 3,</p>
<p>B = I + (I + 3)</p>
<p>so now the equation looks like:</p>
<p>(I + 3) + I + [ I + (I + 3)] = 30</p>
<p>Because it’s all addition, the parentheses don’t matter, now that we are down to just one variable.</p>
<p>So take all the I’s and put them together, and then add up all the numbers to the left of the equal sign. There are 4 I’s, and the numbers add up to 6, so now the equasion looks like this:</p>
<p>4(I) + 6 = 30</p>
<p>Now get rid of the six by subtracting it from both sides.</p>
<p>(You can always get rid of a number on one side by doing the opposite with that number on both sides. If it’s x + 6 on one side, SUBTRACT 6 on both sides. If it’s x/6 on one side, MULTIPLY 6 on both sides, etc…):</p>
<p>4(I) + 6 - 6 = 30 - 6 (or)
4(I) = 24</p>
<p>now, get rid of the four by dividing both sides by four:</p>
<p>4(I)/4 = 24/4 (or)
I = 6</p>
<p>There you have it. ‘I’ equals six!</p>