Question

A 12-team soccer league has $7,260 to award as prize money. the team that finishes in last place will receive $220, and the prize will increase by a fixed amount for each successive place.

How much prize money will the first-place team receive?
What is the difference in prize money between successive prizes?

Answer 1

Answer: $ 990

Explanation:

Since, the total number players, n = 12,

The least amount got by one team, a= $ 220

Let there is a successive difference of d,

Thus, the given situation forms an AP,

In which sum of the AP,
`S_n= (12)/(2)[2* 220 + (12-1)d]`

But, According to the question,

`S_n = $ 7260`

⇒
`(12)/(2)[2* 220 + (12-1)d]=7260`

`6[440 + (11)d]=7260`

`440 + 11 d=1210`

`11 d =770`

`d = 70`

Thus, the successive difference, d = $ 70

⇒ The amount of first price,

`a_(12) = 220 + (12-1)* 70 = 220 + 770 = \$ 990`