Question 1023494
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.