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

Step-by-step 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, $S_n= \frac{12}{2}[2\times 220 + (12-1)d]$

But, According to the question,

$S_n = 7260$

⇒ $\frac{12}{2}[2\times 220 + (12-1)d]=7260$

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

$440 + 11 d=1210$

$11 d =770$

$d = 70$

Thus, the successive difference, d = $ 70

⇒ The amount of first price,

$a_{12} = 220 + (12-1)\times 70 = 220 + 770 = \ 990$