SOLUTION: Two business partners, Ellen and Bob, invested money in their business at a a ratio of 8 to 9. Bob invested the greater amount. The total amount invested was $510. How much did eac

Question 1023494: Two business partners, Ellen and Bob, invested money in their business at a a ratio of 8 to 9. Bob invested the greater amount. The total amount invested was $510. How much did each partner invest?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
e = amount invested by ellen.
b= amount invested by bob.

ratio invested at a rate of 8 to 9, where bob invested the larger amount.

ratio is:

e/b = 8/9

total amount invested is 510.

this means that e + b = 510.

from e/b = 8/9, solve for e to get e = 8b/9

raplace e with 8b/9 in the equation of e + b = 510 to get:

8b/9 + b = 510

multiply both sides of the equation by 9 to remove the denominator and you get:

8b + 9b = 4590.

combine like terms to get 17b = 4590.

divide both sides by 17 to get b = 270.

since e = 8b/9, then e must be equal to 8*270/9 = 8*30 = 240.

ellen invested 240 and bob invested 270.

total invested is 240 + 270 = 510.

ratio of investment by ellen to investment by bob is 240 / 270 = 24 / 27 = 8 / 9.

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