Question

1. A man divides P10,000 in two investments, one at 10% and the other at 30%. Find how much is invested at each rate so that the two investments produce the same income annually.

Answer 1

seems you're back...

Answer 2

HAHA .. o'yeah. :))

Answer 3

Are you supposed to use systems here?

Answer 4

yes..

Answer 5

x and y... suppose he divided the 10000 into two portions, x and y...

Answer 6

So we know for sure that
x + y = 10000
yes?

Answer 7

ehe? we will use x and y??

Answer 8

Well, what do you want?
a and b?
p and q?

You said use systems...

Answer 9

ahh.. haha! :)) nvm,, i'm wrong..

Answer 10

huh?
So... do we continue?

Answer 11

yes.. continue..

Answer 12

x + y = 10000
we need another equation... how to find one?

Answer 13

ahm,, by using the 2 investments??

Answer 14

mhmm... so, the two investments produce the same income annually...

Answer 15

aha! then?

Answer 16

What's the income for the x?

Answer 17

the amount invested at 10%?

Answer 18

Whichever, it doesn't really matter... suppose x was the amount invested at 10 % then...

Answer 19

hm.. i don't know the next..

Answer 20

How much does x earn after a year? 10% of x correct?
So
0.1x

Answer 21

the amount y is invested at 30% so how much does it earn?

Answer 22

10000-0.1x?

Answer 23

no... :/
0.3y

Answer 24

ah.. i got it.. :)) sorry.. :(

Answer 25

So, they have the same income, so you have
0.1x = 0.3y
along with
x + y = 10000
now solve the system :P

Answer 26

just substitute???

Answer 27

Whatever works... for
0.1x = 0.3y
you can ease it up by multiplying both sides by 10
x = 3y

now it's simpler.
Now solve...

Answer 28

y= 2500 and x=7500 .. ? right?

Answer 29

there you go.

Answer 30

eh, how about if we will use 1 variable only on that problem??

Answer 31

Well, just downright divide the 10000 into two parts, x and the rest, which is 10000-x.
And you know that
0.1(x) = 0.3(10000-x)
you'll arrive at the same answer...

Answer 32

ahh.. owkie. :) thank you. :)