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Luke and Owen have \$100$100dollar sign, 100 each. Their friend offered to invest their money, promising to return a sum rrr times as great as what they invested. Luke was suspicious, so he invested \$10$10dollar sign, 10 only, but Owen invested his entire \$100$100dollar sign, 100. Fortunately, the friend did indeed return a sum rrr times as great to each.
They decided to make another investment. This time, Owen invested all of the money returned to him, and Luke invested the money returned to him and the remaining \$90$90dollar sign, 90. Again, they got a sum rrr times as great as what they invested. In the end, Owen had \$337.50$337.50dollar sign, 337, point, 50 more than Luke.
Write an equation in terms of rrr that models the situation.

Respuesta :

Answer:

100r^2=10r^2+90r+337.50

Step-by-step explanation:

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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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