Question

John took money out of his account. He bought a radio for $108. He used 5/9 of what was left for presents and then put 5/6 of the leftover into another account and gave away the remaining $80 to charity. How much did he start with?

Answer 1

help

Answer 2

found you

Answer 3

Ok, let's denote $ he start with as X

Answer 4

ok

Answer 5

Since he bought the radio he has less money. $108 less money
so
x-108

make sense so far?

Answer 6

ok

Answer 7

let's go to next part of the question.

" He used 5/9 of what was left for presents"

The leftover is x-108. So 5/9 of left over is 5/9(x-108 )

good?

Answer 8

good

Answer 9

So money left after buying the radio is( x-180)
and he spend 5/9 of it. So we subtract.

\[(x-180)-\frac{5}{9}(x-180)\]
We can factor to make it look neat
\[(x-180)(1-\frac{5}{9})\]
\[(x-180)(\frac{4}{9})\]

So this is how much money he has left after he bought the radio,use money for the present. Does this make sense?

Answer 10

no--back up, to the (x-108) -5/9(x-108)

Answer 11

(x-108) is how much he has left after buying the radio. He used 5/9 of left over to buy present. So we do (x-108) -5/9(x-108) to get new leftover

Answer 12

Would that be -5/9x + 60

Answer 13

I see you multiplied it ,yes

Answer 14

5/9 * 108

Answer 15

that's correct so subtract -5/9x + 60 from (x-108) to get new left over
x-108-5/9x+60

Answer 16

I factored it, instead of multiplying out

Answer 17

clear?

Answer 18

what next

Answer 19

"then put 5/6 of the leftover into another account"
\[ (x-108-\frac{5}{9}x+60) -\frac{5}{6}(x-108-\frac{5}{9}x+60)\]

Answer 20

Any question?

Answer 21

whereis the 80 that is left

Answer 22

I am not there yet

Answer 23

ok sorry

Answer 24

But so far so good right?

Answer 25

ok

Answer 26

" gave away the remaining $80 to charity"

This part tell us that he has 80 remaining after buying radio,buying present, putting money in another account.
So we may set the previous equation equals to 80

\[(x−108−\frac{5}{9}x+60)−\frac{5}{6}(x−108−\frac{5}{9}x+60)=80\]

Now you are all set to solve for x, just some algebra

Answer 27

don't lave me now__I have stressed over this thing enough

Answer 28

You solve for x; I will too then we will compare result

Answer 29

* Tip
First add like term inside the parenthesis before distributing

Answer 30

It isn't working!!

Answer 31

what do you mean?

Answer 32

it is supposed to come out to 1188 and I'm not getting it.

Answer 33

That's what I got

Answer 34

did you do the sectios separate or together

Answer 35

I do not have a math gene in my body

Answer 36

\[\left(x-108-\frac{5}{9}x+60\right)-\frac{5}{6}\left(x-108-\frac{5}{9}x+60\right)\text{==}80\]

Add like term inside the parethesis

\[(-48+\frac{4 x}{9})-\frac{5}{6}(-48+\frac{4 x}{9})==80\]

\[(-48+\frac{4 x}{9}+40-\frac{10 x}{27})==80\]
\[-8+\frac{2 x}{27}=80\]
\[\frac{2 x}{27}=88\]
\[{2 x}=2376\]
\[{2 x}=2376\]
X=1128

Answer 37

2x=2376
x=1188

Answer 38

This I understand___I just had to see my error__it was the algebra--I did not combine the x's properly.

Answer 39

You have lifted a weight off my shoulders.

Answer 40

Yeah, be careful with algebra, use calculator if you are allowed

Answer 41

I will--exam is tomorrow

Answer 42

What grade?

Answer 43

It is a college course for elementary education. I need it to graduate next month.

Answer 44

It is online and I don't get much feedback.

Answer 45

Good luck on the test tomorrow.

Answer 46

Thank you again. good nite