We invested $10000 into two bank accounts. One account earns 14% per year, the other account earns 8% per year. How much did we invest into each account if after
the first year, the combined interest from the two accounts is $1238?

HELP ME

Hi, there--

THE PROBLEM:

We invested $10,000 in 2 bank accounts. One account earns 14% per year the other earns 8%

per year. How much did we invest into each account if after the first year, the combined

interest from the 2 accounts is $1238?

A SOLUTION:

Define Variables:

Let x be the amount you originally invested in the first account.

Let y be the amount you originally invested in the second account.

Write Expressions and Equations:

Since you invested a total of $10,00 in two accounts. An equation that represents this is

x + y = 10000

One account (say the first one) earns 14% per year. Recall that the decimal form of 14% is

0.14. An expression for the amount of interest you earn after the first year in this account is

0.14x.

The other account earns 8% per year. The decimal representation of 8% is 0.08. The amount

of interest you earn after one year in this account is 0.08y.

The combine interest from both account after one year is $1238. An equation representing

the total interest earned is

0.14x + 0.08y = 1238

Now we have a system of two equations with two variables. We can solve for x and y. Rewrite

the first equation in "y=" form.

x + y = 10000

y = 10000 - x

Substitute 10000-x for y in the second equation.

0.14x + 0.08y = 1238

0.14x + 0.08(10000 - x) = 1238

Solve this equation for x. Use the Distributive Property to clear parentheses.

0.14x + 800 - 0.08x = 1238

Combine like terms (0.14x-0.08x is 0.06x).

0.06x + 800 = 1238

Subtract 800 to both sides to isolate x on the left.

0.06x = 1238 - 800

0.06x = 438

Divide both sides of the equation by 0.06.

x = 438/0.06

x = 7300

In the context of this problem, x=7300 means that you invested $7300 in the first account.

Since you invested a total of $10000, you invested 10000-7300=$2700 in the second account.

Check your work by verifying that these amounts will yield the correct amount of interest.

Substitute 7300 for x and 2700 for y in the interest equation.

0.14x + 0.08y = 1238

0.14(7300) + 0.08(2700) = 1238

1022 + 216 = 1238

1238 = 1238

Check!

Hope this helps! Feel free to email if you have any questions about the

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}