Ann has $8 000 that he plans to split into two investments?

2015-11-23 8:41 pm
he wrote the following two equations to represent the internet He will earn from each of the two investment options

2000A+6000B=520
4000A+4000B =480
Determine the interest rates A and B as percentages

回答 (3)

2015-11-23 9:17 pm
2000A+ 6000B=520=> 4000A + 12000B=1040(1). ;4000A+4000B= 480 (2)
Subtract (2) from (1): 8000B= 560 => B= 0.07 = 7%. Substitute B into (1):
2000A +6000(7/100)= 520 => 2000A= 520 - 420 = 100 =>. A = 100/2000 = 0.05 = 5%
2015-11-23 8:47 pm
Two times the first equation less the second equation will eliminate A.
.. 2(2000A + 6000B) - (4000A + 4000B) = 2(520) - (480)
.. 8000B = 560
.. B = 560/8000 = 0.07
.. A = 0.12 - B ... from the second equation divided by 4000
.. A = .05

A is 5%, B is 7%.
2015-11-23 8:46 pm
You have two equations and two variables. This looks a bit tricky to do by substitution, so let's use elimination.

Multiply the first equation (both sides, of course!) by -2. You'll see why I picked this number in a moment.

-2 * (2000A + 6000B) = -2 * (520)
-4000A - 12000B = -1040

Now we can add this to our second equation!
-4000A - 12000B = -1040
4000A + 4000B = 480
__________________
0A - 8000B = -560

Now we have one equation and one variable. (That's why I picked -2 for the first equation, because I knew it would cause the As to cancel out.)

-8000B = -560
B = -560/-8000
B = 0.07, or 7%

Now we can plug that back into either equation and solve for A. Let's use the second one, though either would work.

4000A + 4000B = 480
4000A + 4000(0.07) = 480
4000A + 280 = 480
4000A = 200
A = 0.05, or 5%

That's called solving by elimination. If you like, you can try again, but this time multiply the top equation by -2 and the bottom equation by 3, then add together...that will eliminate the Bs. You should get the same answer!


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