Final Review Question 15
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Problem:
At the soccer team pizza party, the kids who came early evenly split the cost of the pizza, which altogether cost $120. Four late kids came, and they pitched in to share the cost of the pizza, with each of them paying $0.25 to each of the kids who were originally there. In the end, everyone paid the same amount, and the contribution of the original kids dropped by 20%. How many kids were there in the beginning?Explanation:
Each of the original kids received a total of $1 from the late kids. So, the effect of the late kids coming was to reduce the cost per person by exactly $1. Let n be the number of kids in the beginning. Then
120/n-120/(n+4)=1
Combining the two fractions by making a common denominator of n(n+4), we get:
120(n+4)/n(n+4)-120n/n(n+4)=1
(120n+480-120n)/n(n+4)=1
The n terms in the numerator cancel out, and we are left with
480/n(n+4)=1
n(n+4)=480
By solving the quadratic equation, or by guessing and checking, we see that n=20 works, since 20*(20+4)=480. The answer is n=20.Wasn't the 20% part ignored? Besides, since 120/20=6 120/24=5, and 80% of 6 isn't 5, shouldn't there be no answer?
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@spaceblastxy1428 Thank you so much for noticing this! Yes, this in a error in the question, which was carried over from the Module 1 Placement Exam question with the same idea:
"At the soccer team pizza party, the kids who came early evenly split the costof the pizza, which altogether cost \(\$80.\) Four late kids came, and they pitched in to share the cost of the pizza, with each of them paying \(\$0.25\)
to each of the kids who were originally there, so that in the end everyone paid the same amount. How many kids were there in the beginning?"I've fixed this problem, so the \(20\%\) shouldn't be there anymore. I'm very sorry for the confusion and I really appreciate you taking the time to tell us so that we can fix it!
(By the way, if you want to learn how to type math in the forum, there's a quick forum guide here.
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