Prize

Algebra Level 2

Total prize money of $ 5000 \$5000 is to be divided among 8 8 contestants so that the 8 t h 8^{th} placer will receive $ 100 \$100 and each other a fixed amount more than the preceding person. What prize money goes to the 1 s t 1^{st} placer?


The answer is 1150.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Using the formula for the sum of terms in an arithmetic progression, we have

S = n 2 ( a 1 + a n ) S=\dfrac{n}{2}(a_1+a_n)

5000 = 8 2 ( a 1 + 100 ) 5000=\dfrac{8}{2}(a_1+100)

10000 = 8 ( a 1 + 100 10000=8(a_1+100

10000 8 = a 1 = 100 \dfrac{10000}{8}=a_1=100

10000 8 − 100 = a 1 \dfrac{10000}{8}-100=a_1

a 1 = a_1= 1150 \color{#D61F06}\boxed{\large 1150}

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