SOLUTION: Kyle earned a total of $12500 for drawing 5 pictures. The money he received for each picture was $28 more than the money he received from the previous picture. In other words, he w

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Question 477706: Kyle earned a total of $12500 for drawing 5 pictures. The money he received for each picture was $28 more than the money he received from the previous picture. In other words, he was paid $28 more for the second picture than the first, $28 more for the third than the second, and so forth. How much was he paid for the 1st picture?
Answer by Mathmama(2) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is an example of an arithmetic series
Here the first term "a" is the price of the first picture

the common difference "d" is $28
the number of terms "n" is 5

The series is
a + (a + 28) + (a + 28 + 28) + (a + 28 + 28 + 28)+ (a + 28 + 28 + 28 + 28)

The Sum of first n terms of an arithmetic series is given by

S%5Bn%5D+=++n+%28a+%2B+%28n-1%29d%2F2%29
The sum of the prices of the 5 pictures is S%5B5%5D = 12500
S%5B5%5D++=++5%28a+%2B%285-1%2928%2F2%29 = 12500
S%5B5%5D+=+5%28a+%2B+4+%2A28%2F2%29 = 12500
S%5B5%5D+=+5%28a+%2B+56%29 = 12500
5(a + 56) = 12500
To solve for "a" - the price of the first picture
Divide both sides by 5

a + 56 = 12500/5 = 2500
Subtract 56 from both sides

a = 2500 - 56

a = $2444
Therefore the price for the first picture is $2,444.