Maths
posted by Mathshelpme .
When J gives A $6, they will both have the same amount. When A gives J $6, she will have 1/3 of J's amount. What are the amounts they both have at first?( please do not solve by algebra, i have not been taught algebra)

From the first sentence I can tell that J must have $12 more than A
Also from the second sentence A must have at least $6
so form two columns of possible amounts, starting with A having 6
A J
6 18
7 19
8 20
9 21
10 22
11 23
12 24
13 25
14 26
15 27
16 28
17 29
18 30
19 31
...
Now metally take 6 away from A and add 6 to J
when will the first value be 1/3 of the 2nd?
how about 18 and 30
(186) = (1/3)(30+6) > 12 = (1/3) of 36
I bet you can't wait to learn Algebra. You will be so surprised how really easy these questions become.
J6 = A+6 > JA = 12
A6 = (1/3)(J+6)
3A  18 = J+6
3A  J = 24
3A  J = 24
A + J = 12
add them
2A = 36
A = 18, then J = A+12 = 30 
ok. no algebra*
We know that J has $12 more than A. That's because when J is $6 less, it is the same as the new A, which is $6 more.
J can't have just $12, because that would mean that A started with 0, and could not give 6 to J.
A and J must both be multiples of $6, since we're juggling $6 chunks.
So, suppose A = 12. That would make J=24, but 126=6 is not 1/3 of 24+6=30.
If A=18, J=30 and 186=12 is 1/3 of 30+6=36.
*
But all of this reasoning is just doing algebra in your head. It's never to soon to learn a little algebra, so you might as well start now.
Algebra just gives you a way of writing down number facts so you don't have to keep track of everything in your head.
Let J and A represent the two starting amounts.
J gives A $6, so now we have
J6 = A+6
If you have a true sentence (or equation), it stays true as long as, if you make changes, you make the same changes to both sides of the equation.
For example, if J is 5 years older than A, she will still be 5 years older a year from now. That is, if
J = A+5
next year,
J+1 = A+5+1
In our problem, we have
J6 = A+6
If you add 6 to both sides, you get J by herself:
J6+6 = A+6+6
J = A+12
Now, if we have two unknown numbers, we need to know two independent things about how they fit together. Our second thing is: If A gives J $6, she has 1/3 of J's new amount. Or, avoiding fractions, J will then have 3 times as much as A. In symbols,
J+6 = 3 * (A6)
Here * means times. To get rid of the parentheses, you need to know about how multiplication distributes over addition. You already know this, but maybe not by name. If someone asks you to add 300 and 400, you have no trouble coming up with 700 as the answer. In your head, you probably say, well considering hundreds, 3+4=7. In symbols,
300 + 400 = 3*100 + 4*100 = (3+4)*100
In other words, you do what's in the parentheses first, then do the multiplication. In our case, we have
J+6 = 3*(A6)
J+6 = 3A  3*6
J+6 = 3A  18
Add 18 to both sides:
J+24 = 3A
Now, we know J=A+12. Wherever we have J, we can just as well use A+12. We can make that substitution, and we now have
A+12 + 24 = 3A
A + 36 = 3A
Now, we need to get all the A's together, so subtract A from both sides.
AA + 36 = 3A  A
But, AA = 0, and 3AA = 2A
So, now we have
36 = 2A
In words, 36 is twice as much as A.
so, A is just half of 36 = 18.
Since J=A+12, J=18+12 = 30.
Congratulations. While there are still some gaps to fill in, you've just covered half a semester of algebra.
Respond to this Question
Similar Questions

Math riddle, I need help!!
Person A has one amount of money in his pocket, Person B has one amount of money in his pocket. If person A gives X amount to person B, person B will end up with 3 times more money than person A. However if person B gives the same … 
maths
1/5 of Jane's money is equal to 1/3 of Sam's money. The difference in their amount is 1/2 of Adam's money. If Adam gives $120 to Sam, Sam will have the same amount of money as Jane. How much do the 3 people have altogether? 
maths urgent
1/5 of J's money is equal to 1/3 of S's money. The difference in their amount is 1/2 of A's money. If Adam gives $120 to S, S will have the same amount of money as J. How much do the 3 people have altogether? 
Algebra
Natalie has some nickles, Dirk has some dimes, and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters. If Natalie gives Dirk a nickel, Dirk gives Quincy a dime, and Quincy gives Natalie a quarter, they will … 
maths
Robin says , 'If Jai gives me Rs. 40, he will have half as much as Atul , but if Atul gives me Rs. 20, then the three of us will all have the same amount. ' What is the total amount of money that Robin, Jai and Atul have between them … 
math
There are 10 children (aged 1 to 10 years) who have equal amounts of money. In the first transaction the eldest child gives one rupee to every child younger to him. In the second transaction, the second eldest child gives one rupee … 
algebra
If Will gives Molly $9, he will have the same amount of money as her. If Molly gives Will $9, the ratio of the money she has to the money Will has will be 1 : 2. How much money does Will have in the beginning? 
Urgent due tomorrow Algebra
Tom, Dick, and Harry are three brothers and have $107.60 together. Tom feels sorry for hairy because he has less money than Tom. So Tom gives harry $2.10 so they both will have the same amount after the transfer. Dick doesn't know … 
Algebra Help ASAP Please
Tom, Dick, and Harry are three brothers and have $107.60 together. Tom feels sorry for hairy because he has less money than Tom. So Tom gives harry $2.10 so they both will have the same amount after the transfer. Dick doesn't know … 
Algebra Help please
Tom, Dick, and Harry are three brothers and have $107.60 together. Tom feels sorry for hairy because he has less money than Tom. So Tom gives harry $2.10 so they both will have the same amount after the transfer. Dick doesn't know …