SOLUTION: If you could please show me the formula, I think I could solve it myself. A teacher has the choice of two investment plans, one at 11% and the other at 13%. If the same amount inve

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Question 246287: If you could please show me the formula, I think I could solve it myself. A teacher has the choice of two investment plans, one at 11% and the other at 13%. If the same amount invested at 13% yields 150.00 more per year, how much does she have to invest?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.