Dan made $9000 from his job then invested 10% and at the rest 9%. He made a total of $870 how much was the invested at 9%

Question

Please help

Answer 1

 

Please check the statement of the problem. The numbers do not work out.

If he invests all of it at 10%, the return is going to be $90. Perhaps you meant

he earned $9000. Anyways here's the best we can do for you.

 

Let P be the principal amount and I be the interest returned. Assuming he invested the amounts in

different accounts returning 10% and 9 respsectfully, here are the two equations.

Note that 10%=0.1 and 9% = 0.09. These decimals will be cleared by multiplying the second

equation by 100.

 

X + Y = P

 

0.1X + 0.09Y = I --> 10X + 9Y = 100I  <-- clears the decimals by multiplying by 100

 

 

 

Solving the first equation for Y --->  Y = P - X

Subsituting into the second equation:

 

 10X + 9( P - X) = 100I

 

10X + 9P - 9X = 100I

 

X + 9P = 100I

 

X = 100I - 9P <-- THIS IS THE AMOUNT AT 10%; 

 

Then Y = P - X = P - (100I - 9P)

                      = P - 100I + 9P

                      = 10P  - 100I  <-- THIS IS THE AMOUNT at 9%; use this one!!!!

 

So when you get the right numbers, use that equation.

For example, let's say he earned a principal of $9000 with a return of 870.

 

Then P=9000 and I = 870.

Plugging them into the formulas I derived for you, he earned

 

X = 100I - 9P = 100*870 - 9*9000

                    = 87000 - 81000

                    = 6000   <--- invested at 10%

 

Y =  10P - 100I = 10*9000 - 100*870

                       = 90000 - 87000

                       = 3000 <--- invested at 9%

 

Notice they add up to 9000.

This is the best that can be done with what is given.