Question 246287
I would assume you could possibly solve this as follows:


Let x = the amount she has to invest.


x * 1.11 = y


x * 1.13 = y + 150


You can solve for x or y in each equation.


This would be your choice.


I'll solve for x in terms of y first.


Then I'll make those equations equal to each other and then solve for y.


Once I've solved for y, I'll then go back in and solve for x.


IF YOU JUST WANT THE EQUATIONS THEN YOU CAN STOP HERE AND SOLVE IT YOURSELF.


I SOLVED IT DOWN BELOW.   YOU CAN USE THAT FOR REFERENCE IF YOU WISH.


Your first equation is x * 1.11 = y


divide both sides of this equation by 1.11 to get x = y/1.11


Your second equation is x * 1.13 = y + 150


divide both sides of this equation by 1.13 to get x = (y+150)/1.13


You now have two equations, both equal to x.


You have:


x = y/1.11 and x = (y+150)/1.13


Since they both equal to x, then they both equal to each other so you get:


y/1.11 = (y+150)/1.13


multiply both sides of the equation by (1.11)*(1.13) to get:


1.13*y = 1.11*(y+150)


simplify by removing parentheses to get:


1.13*y = 1.11*y + 1.11*150


subtract 1.11*y from both sides of equation to get:


1.13*y - 1.11*y = 1.11*150


simplify further by combining like terms and performing indicated operations to get:


.02*y = 166.5


divide both sides of equation by .02 to get:


y = 166.5/.02 = 8325


now that you know y, you can solve for x.


your first equation is 1.11 * x = y


this means that x = 8325/1.11 = 7500


your second equation is 1.13 * x = y + 150


this becomes 1.13 * x = 8475


this means that x = 8475 / 1.13 = 7500


x is equal to 7500 in both equations, so the value for y is good.


substitute for x in your original equations to get:


1.11 * x = 8325
1.13 * x = 8475


8475 - 8325 = 150 so we're good all around.