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An equation in terms of r which models the situation described is : 100r² = 10r² + 90r - 337.50
First investment :
Luke:
Total amount had = $100
Amount invested = $10
Amount left = $100 - $10 = $90
Return = r times the amount invested = (10 × r) = 10r
Owen:
Total amount had = $100
Amount invested = $100
Return = r times the amount invested = (100 × r) = 100r
Second investment :
Luke :
Amount invested = Return on first + amount left = 10r + 90
Return is r times the amount invested :
Return on second investment = (10r + 90) × r = (10r² + 90r)
Total amount earned after both investment = 10r² + 90r
Owen :
Amount invested = Return on first = 100r
Return is r times the amount invested :
Return on second investment = (100r × r) = 100r²
Total amount earned after both investment = 100r²
Owen made 337.50 more than Luke ; This means that :
Total earned by Owen = Total earned by Luke + 337.50
100r² = 10r² + 90r + 337.50
Hence, the equation in terms of r is : 100r² = 10r² + 90r - 337.50
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