SOLUTION: I need help with this particular question, thank you for your help in advance! Determine the 2005 income for a particular company for each quarter from the data in the graph when

Question 1123408: I need help with this particular question, thank you for your help in advance!
Determine the 2005 income for a particular company for each quarter from the data in the graph when S = 375, a = 15, b = 7, and c = 7. $a million more than first quarter, $b million less than twice the first quarter, and $c million more than four times first quarter, S is the net income/ $S million
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Determine the 2005 income for a particular company for each quarter from the data in the graph when S = 375, a = 15, b = 7, and c = 7. $a million more than first quarter, $b million less than twice the first quarter, and $c million more than four times first quarter, S is the net income $S million.

total net income is 375 million.
a = 15
b = 7
c = 7

let the net income for the first quarter = f.

all numbers appear to be in millions.

a = f + 15 = the net income for the second quarter.
b = 2f - 7 = the net income for the third quarter.
c = 4f + 7 = the net income for the fourth quarter.

the total net income is 375 which means that f + a + b + c = 375

since a = f + 15 and b = 2f - 7 and c = 4f + 7, you can relace a,b,c with their respective values in terms of f to get:

f + (f + 15) + (2f - 7) + (4f + 7) = 375

simplify to get f + f + 15 + 2f - 7 + 4f + 7 = 375

combine like terms to get 8f + 15 = 375

subtract 15 from both sides of this equation to get 8f = 360

divide both sides of this equation by 8 to get f = 360 / 8 = 45.

the first quarter net income was 45.

the second quarter net income was 45 + 15 = 60

the third quarter net income was 2 * 45 - 7 = 90 - 7 = 83

the fourth quarter net incomes was 4 * 45 + 7 = 180 + 7 = 187.

the total net income for the year was 45 + 60 + 83 + 187 = 375.

solution looks good if i understood the problem correctly.

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