Robin split a total of $24,000 between two investments, X and Y. If investment Y earns 7% simple annual interest, how much did Robin put into investment Y?
(1) Each investment earns the same dollar amount of interest annually.
(2) Investment X earns 5% simple annual interest.
From the question I see that X + Y = 24000, so X = 24000 - Y and Y = 24000 - X
From (1) I can set the equation that (24000-x)(1.07) = (24000-y)(% interest of x) --> Since I don't know the interest of X investment, this is insufficient
From (2) I now know the interest of X, so (24000-x)(1.07) = (24000-y)(1.05). Is the correct approach then to solve for X, then plug the value of X in terms of Y into the X+Y = 24000 equation and solve for Y?
The answer is that both statements together are sufficient, i just want to make sure I solved it correctly.
I think sometimes I get confused when is it possible to be able to solve for an equation with two unknown variables.
(1) Each investment earns the same dollar amount of interest annually.
(2) Investment X earns 5% simple annual interest.
From the question I see that X + Y = 24000, so X = 24000 - Y and Y = 24000 - X
From (1) I can set the equation that (24000-x)(1.07) = (24000-y)(% interest of x) --> Since I don't know the interest of X investment, this is insufficient
From (2) I now know the interest of X, so (24000-x)(1.07) = (24000-y)(1.05). Is the correct approach then to solve for X, then plug the value of X in terms of Y into the X+Y = 24000 equation and solve for Y?
The answer is that both statements together are sufficient, i just want to make sure I solved it correctly.
I think sometimes I get confused when is it possible to be able to solve for an equation with two unknown variables.
