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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?

Respuesta :

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, [tex]S_n= \frac{12}{2}[2\times 220 + (12-1)d][/tex]

But, According to the question,

[tex]S_n = $ 7260[/tex]

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

[tex]6[440 + (11)d]=7260[/tex]

[tex]440 + 11 d=1210[/tex]

[tex] 11 d =770[/tex]

[tex]d = 70[/tex]

Thus, the successive difference, d = $ 70

⇒ The amount of first price,

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


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