Prize Money for 1st Place in 16 Team Bowling League: $1,930

It asks for the amount the first-place team will receive. You need to use the formula for the sum of an arithmetic sequence, which is (n/2)(a1 + an), where n is the number of terms, a1 is the first term, and an is the nth term. In this case, n = 16, a1 = 275, and an = a1 + (n-1)d. So, the first-place team will receive (16/2)(275 + (16-1)d) = 8000. Simplify the equation and solve for d to find the common difference, then plug that value back into the formula to find the first-place amount. In summary
  • #1
r-soy
172
1
A 16 team bowling league has $ 8,000 to be awarded as prize money. If the last place
team is awarded $ 275 in prize money and the award increases by the same amount for
each successive finishing place, how much will the first place team receive?

My answer :

a1 -- ? D = 275

an = a1=(n-1 ) d = 275
an = a1 + ( ( 16 - 1 ) d = 8000
a1(15)(275) = 8000
a14125 = 8000
a1 = 1.93
 
Physics news on Phys.org
  • #2


Does that even make sense to you? You are saying that if the last place team won $275, the first place team must have won $ 1.93!

You are told that [itex]a_1= 275[/itex]- "If the last place team is awarded $ 275 in prize money" so 275 is the smallest amount in this arithmetic sequence, not the common difference.

If an arithmetic sequence has initial amount [itex]a_1[/itex] and common difference d, then the nth number is [itex]a_1+ (n-1)d[/itex] and the sum is [itex](a_1+ (n-1)d/2)n[/itex]. You are told that [itex]a_1= 275[/itex], n= 16, and that the sum is 8000 so you can solve for d.
 
  • #3


see I write two answer see which one is correct :

An = 2a1 + ( n - 1 ) d
a16 = 275(15) d = 80000
4125d = 80000
d = 8000/4125 = 1.9
-------------------------------
-----------------------------
Sn = n/2( 2.a1 ( n - 1 ) d
16/2(2(275)(15) d ) = 8000
8(8250d) = 80000
d = 8000/60000 = 0.12
 
  • #4


Neither of those is correct! You have solved for d and the question does not ask for d.
 

What is the total amount of prize money for 1st place in a 16 team bowling league?

The total amount of prize money for 1st place in a 16 team bowling league is $1,930.

How many teams are in the bowling league?

There are a total of 16 teams in the bowling league.

How is the prize money distributed among the winning team?

The $1,930 prize money is typically divided among the members of the winning team, with each member receiving an equal share.

Is there a second place prize?

It is not specified whether there is a second place prize for this particular bowling league. The prize money may only be awarded to the 1st place team.

Is the prize money subject to taxes?

The answer to this question may vary depending on the specific rules and regulations of the bowling league and the country or state in which it is located. It is recommended to consult with a tax professional for accurate information.

Similar threads

  • General Discussion
Replies
1
Views
635
  • Computing and Technology
Replies
5
Views
2K
Replies
8
Views
12K
Replies
9
Views
2K
  • Precalculus Mathematics Homework Help
Replies
13
Views
4K
  • Math Proof Training and Practice
6
Replies
175
Views
20K
  • Art, Music, History, and Linguistics
Replies
1
Views
1K
Replies
1
Views
1K
  • General Discussion
Replies
4
Views
4K
  • STEM Academic Advising
Replies
10
Views
5K
Back
Top