Question

how do i even start this?
Paul invested twice as much money in an account paying 4% interest than he did in an account paying 2% interest. If the total interest paid was $250, how much did he invest in each?

Answer 1

You start by representing the unknown values...
for instance
We can let
x = how much Paul invested in the 2% interest account.

If that were the case, how do you represent how much Paul invested in the 4% account? :)

Answer 2

2x+.04

Answer 3

no, just 2x. It was specified that Paul invested TWICE as much in that particular account, so it's 2x.

Get it? :)

Answer 4

yeah

Answer 5

Ok. So the interest gained in the 2% account is...?

Answer 6

125

Answer 7

what? How do you figure that?

Answer 8

idk how to figure it out

Answer 9

It's 2% of x (which is how much he deposited in that account)

Answer 10

so x divided by .02

Answer 11

i'm supposed to solve this by using a system of equations

Answer 12

Well, that changes things... but the essence is the same...
We can let
x = amount he deposited in the 2% account
y = amount he deposited in the 4% account

ok? :)

Answer 13

okay

Answer 14

so, the interest in the 2% account is 2% of x, right?
or
0.02x
any questions? :)

Answer 15

nope i understandthat

Answer 16

And the interest in the 4% account is...?

Answer 17

.04y

Answer 18

ok, so the total interest all in all, which is basically the sum of
0.02x and 0.04y, is...?

Answer 19

250

Answer 20

so... we have one equation
0.02x + 0.04y = 250

We need another, can you get one? :)

Answer 21

we know that what he invested in the 4% account is TWICE what he deposited in the 2% account.
So y = 2x, aye? :)

Answer 22

yeah

Answer 23

so, you now have two equations, can you solve it from here? :)

Answer 24

i did it wrong.
0.02x+0.04(2x)=250
0.04x+0.04=250

Answer 25

ohhhh no

Answer 26

You forgot to retain the x... look again :)

Answer 27

so it's 0.04x+0.08x=250

Answer 28

that's right. Now figure it :)

Answer 29

Wait NO

Answer 30

Why did the 0.02x become 0.04x?

Answer 31

just kidding

Answer 32

so .1x=250

Answer 33

That's right :) now solve for x

Answer 34

2500

Answer 35

Nicely done. Now, with y = 2x, what is y?

Answer 36

5000

Answer 37

And you now have your values :)

Answer 38

THANkyou! can you help me with another problem you're really good at explaining things

Answer 39

Sure, hit me :)

Answer 40

Chuck and Dana agree to meet in chicago for the weekend. Chuck travels 220 miles in the same time that Dana travels 205 miles. if Chuck's rate of travel is 3mph more than Dana's then at what rate does chuck travel?

Answer 41

Are you to use systems again?

Answer 42

yes

Answer 43

Hang on a sec

Answer 44

I can solve it, but not with systems, just a basic linear equation in one variable.

Answer 45

Well, actually, no, It won't be linear.

Answer 46

oh

Answer 47

i guess still show me?

Answer 48

Hang on, I was wrong, sorry

Answer 49

All right, systems is the way to go here, ready? This might be tricky...

Answer 50

yes

Answer 51

First, we let x = Chuck's rate
and we let y = Dana's rate, ok?

Answer 52

yes

Answer 53

We know that Chuck's rate is 3mph more than Dana's, so
x = y + 3
any questions? :)

Answer 54

nope

Answer 55

Ok, we have one equation, we need another, which will be a bit tricky, so pay attention.
You know that speed = distance over time, right?

Answer 56

yeah

Answer 57

So time = distance over speed , right?

Answer 58

yes

Answer 59

so, they arrive at the same time, so time is constant.
The time = Chuck's distance / Chuck's speed
and also
time = Dana's distance / Dana's speed
are you with me so far?

Answer 60

yeah

Answer 61

So
Chuck's distance / Chuck's speed = Dana's distance / Dana's speed
right?

Answer 62

yeah

Answer 63

What distance did Chuck and Dana travel?
220 and 205, right?
And Chuck's speed is x, Dana's speed is y
so you get
\[\frac{220}{x}=\frac{205}{y}\]

Answer 64

There's your second equation, so you have your system, it shouldn't be hard to evaluate Chuck's speed (x)
:D
Have fun

Answer 65

remember
x = y + 3

Answer 66

yes

Answer 67

so go ahead and solve the systems :)

Answer 68

i got 41 for y

Answer 69

and 44 for x

Answer 70

Nicely done :)

Answer 71

thank you! youre really good at explaining i get it when you explain it

Answer 72

For the record, all you needed was the value for x, which you did get, nicely done, and thanks! :)

Answer 73

no problem!