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?(non-algebra solution pls)
Sam's money --- x
Jane's money --- y
y/5 = x/3
3y = 5x
y = 5x/3
Adam's --- z
difference in amount of Sam and Jane = 5x/3 - x
= 2x/3
"The difference in their amount is 1/2 of Adam's money" ---> 2x/3 = (1/2)z
z = 4x/3
after give-away:
Adam has 4x/3 - 120
so 4x/3 - 120 = 2x/3
times 3
4x - 360 = 2x
2x = 360
x = 180
Sam has 180
Jane has 300
Adam has 240 , together they have 720
I am unable to understand the algebra method, could you simplify?
Joi, you need a personal tutor.
To solve this problem without algebra, we can use a method called "plugging in numbers" or "guess and check."
Let's start by assigning a value to Adam's money. Since the difference in their amounts is 1/2 of Adam's money, let's assume Adam has $240.
Now, if Adam gives $120 to Sam, Sam will have the same amount of money as Jane. So, currently, Sam has $120 less than Jane.
Let's continue plugging in numbers. Let's assume Jane has $360. In this case, Sam would have $240 (360 - 120).
Now, let's check if the given condition holds. 1/5 of Jane's money should be equal to 1/3 of Sam's money.
1/5 of $360 is $72.
1/3 of $240 is $80.
Since $72 is not equal to $80, our initial assumption is incorrect.
Let's try plugging in another number. We can assume that Adam has $480, for example.
Following the same steps as before:
Jane has $720 (1.5 times Adam's money as she has 1/2 more than Sam)
Sam has $360 ($480 - $120)
Adam has $480
Now, let's check if 1/5 of Jane's money is equal to 1/3 of Sam's money:
1/5 of $720 is $144.
1/3 of $360 is $120.
Since $144 is indeed equal to $120, our assumption is correct.
Now, we can calculate the total amount of money they have altogether:
Jane: $720
Sam: $360
Adam: $480
Adding all of these amounts together, we get:
$720 + $360 + $480 = $1560
So, the total amount of money the three people have altogether is $1560.