Need help with a level 5 math question! Please help!!

Test Preparation SAT Preparation
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<p>I've been trying so hard to find the solution for the following problem. The answer key states that the answer is 240 but I have no idea how they got to that number. I'd really appreciate it if someone give me a small explanation along with the work involved to get the answer. Thanks!</p>

<p>Question:
All the attendees for a conference arrived by Monday morning. On Monday afternoon, 1/10th of the attendees went home. On Tuesday, 1/3 of the attendees who remained went home. On Wednesday, twice as many attendees as had gone home on Monday went home, leaving 96 attendees at the conference. If no other attendees joined or left during this time, how many attendees were at the conference on Monday morning?</p>

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<p>My approach to the problem,which is incorrect.</p>

<p>x is the full number of people.</p>

<p>x-(0.1x)-(0.9times0.3)-(0.2x)=96</p>

<p>x-0.57x=96</p>

<p>0.43x=96</p>

<p>x=223.255</p>

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<p>Let there be n people to begin with. Following Monday afternoon, there are 9n/10 people left. After people leave on Tuesday, there are 2/3*9n/10=3n/5 people left. Now n/5 people leave (since n/10 people left Monday), leaving 3n/5-n/5=2n/5=96, so n=240.</p>

<p>Edit: The reason that the above is wrong is that 1/3=/=0.3.</p>

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<p>@RandomHSer</p>

<p>I was wondering what was wrong.Thank you!</p>

<p>Dang those careless mistakes! -_-</p>

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<p>@RandomHSer‌ That’s a great way to solve it!! Thank you so much! Now, just out of curiosity, what score did you get on you SAT exam? (or at least the math section)</p>

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<p>I was never a math whiz, I’m over 40 and was able to figure it out.
just work with what you know.
x= all people
1/10x+1/3*9/10x+2/10x+96=x
monday 1/10 of all leave so 1/10x
tuesday 1/3 of all remaining leave so 1/3 of 9/10 which is 3/10x
wednesday twice as many leave as on mon so 2/10x
96 are left so all added together should be x
1/10x + 3/10x +2/10x +96 = x
6/10 x +96 =x
96 = x-6/10x
96 = 4/10x
96 *10/4 =240</p>

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<p>@meumeu I’m pretty sure I’ve made that EXACT mistake at some point. Better to make it here than on a test.</p>

<p>@JohnDoe21 I got a 2300 superscored (2280 single) with a 750 math. None of the mistakes I’ve made on the math section were level 4 or 5s; I just can’t get through 54 questions without a lapse in concentration at some point. I plan to study math despite it being my worst subject on the SAT haha (take that Collegeboard!).</p>