Question

18% and 6% of a sum of money differs by $60. How much is the sum of money?

Answer 1

Call the amount of money X. How much is 18% of X? It is 0.18X.
And how much is 6% of X? It is 0.06X

Now, what's the relationship between
0.18X
0.06X
and
$60
?

Answer 2

0.12 x $60

Answer 3

no

Answer 4

i dont know D:

Answer 5

In terms of the algebraic expression we wrote above, what is
"18% and 6% of a sum of money". The sum of money is X.

Answer 6

18% + 6% = sum of money

Answer 7

0.18X and 0.06X

Now, what is the difference between the two of them?

0.18X - 0.06X

And what amount are we told that is equal to?

Answer 8

0.12

Answer 9

No.

0.18X - 0.06X = 0.12X

And what now is the amount of money we are told that difference is equal to?

Answer 10

$60

Answer 11

Right, so what is the equation you need to solve?

Answer 12

it need to solve the sum of money?

Answer 13

"18% and 6% of a sum of money differs by $60. How much is the sum of money?"

Answer 14

What is the algebraic expression we are using for "the sum of money"? X

What do we know about X?

Answer 15

We know that
0.18X - 0.06X = $60

Answer 16

Now solve that equation for X.

Answer 17

0.12X=$60
60/0.12= X

Answer 18

Yes, but you can't leave the answer that way. Calculate it out.

Answer 19

500 :D
YES YOUR THE BEST TEACHER ONLINE EVER!!

Answer 20

Now verify the result to make sure you got it right.

What is 18% of X?

Answer 21

I Don't get it

Answer 22

18% multiply x

Answer 23

We want to make sure we haven't made a mistake. To do that, we are now working the problem "forwards" to make sure it is consistent with our solution, which was working the problem "backwards".

So working it forwards...
what is 18% of $500? $90
What is 6% of $500? $30

Hence what is the difference of 18% of $500 and 6% of $500? It is
$90 - $30 = $60

Is that consistent with what we were told?

Answer 24

YES SIR :D

Answer 25

Yes it is consistent. Hence we can now say with confidence that $500 is the sum of money and the final answer.

I strongly recommend you do this verification step at the end of all these problems. You will catch many errors this way.

Answer 26

Yes thank you for your recommendation.

Answer 27

Can i ask you something else please

Answer 28

if it's a new question, post it on the left. But in principle, yes.

Answer 29

K Thanks for your help, i don't know what else i should do to give you something back

Answer 30

don't worry. ok, till later

Answer 31

k thank you again

Answer 32

i gave you a medal