Rupan and Hazel had some money. The amount of money Rupan had was 2/7 of Hazel's money. In the following month, the 2 children saved $40 each. Rupan's money was now 2/5 of Hazel's money. How much money did the 2 children have altogether at the end?
What I did so far:
$40*2=$80(both saved)
2/5-2/7=4/35
4u---> $80
1u---> $20
Please tell me if my steps are wrong.
For what does "u" stand? What, exactly, are your steps doing? Why are you subtracting the fractions? What is your logical reasoning for this?
Instead, let's try working with the logic of what they've given you. Since you posted this to "Arithmetic", I'll assume you haven't studied algebra at all yet.
You are given that, originally, Rupan's money was 2/7 of Hazel's money. So draw seven boxes for Hazel's money, and two (of the same size) for Rupan's money.
Then they added forty to each of the totals. Draw another box, alongside the others, and label it "40". So you should have this:
Code:
money:
+-+-+-+-+-+-+-+----+
H: | | | | | | | | 40 |
+-+-+-+-+-+-+-+----+
R: | | | 40 |
+-+-+----+
Alongside these (above and below), draw the larger boxes for the new situation:
Code:
money:
+---+---+---+---+--+
| | | | | |
+-+-+-+-+-+-+-+----+
H: | | | | | | | | 40 |
+-+-+-+-+-+-+-+----+
R: | | | 40 |
+-+-+----+
+---+----+
| | |
+---+----+
(Obviously, the above is not to scale.)
If you subtract R's amount from H's amount (in terms of small boxes and the added 40), you'd be subtracting 2 small boxes and 40 from 7 small boxes and 40, leaving 5 small boxes. You'd also, which is the same thing, be subtracting 2 big boxes from 5 big boxes, leaving 3 big boxes. Then how many small boxes are equal to how many big boxes?
If you multiply this relationship by 5, how many small boxes are equal to how many big boxes?
If you take R's original two small boxes plus the new 40, and multiply this by 5, what do you get? How can you relate this to the previous relationship? Where does this lead?
If you get stuck, please reply with your work and answers for the above questions. Thank you!
