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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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