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Question 1184459: Gillian and Ben had a total of 4850 toys. Ben have 3/7 of his toys to Gillian. She then gave 1/3 of here toys to Ben. The ratio of the number of toys Gillian left to the number of toys Ben left was 2:3.
a) How many toys did Gillian have at the end?
b) How many toys did Ben have at first?
Dear teachers, can help me how to do this? Is ratio working backwards I think.
Found 3 solutions by josgarithmetic, ikleyn, 54929:
Answer by josgarithmetic(39615)   (Show Source):
You can put this solution on YOUR website! Much should be possible in just your first two sentences (with some writing-adjustment).
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Gillian and Ben had a total of 4850 toys. Ben had 3/7 as many as Gillian.
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variable g for number of Gillian's toys at the start, then
Ben had (3/7)g toys at the start.
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Answer by ikleyn(52772)  (Show Source):
You can put this solution on YOUR website! .
UNFORTUNATELY, your writing is SO INACCURATE, that MISREPRESENTS the meaning of the problem.
THEREFORE, below I placed my editing of your post, with my corrections.
Gillian and Ben had a total of 4850 toys.
Ben  GAVE 3/7 of his toys to Gillian.
She then gave 1/3 of  HER toys to Ben.
The ratio of the number of toys Gillian left to the number of toys Ben  finally had was 2:3.
a) How many toys did Gillian have at the end?
b) How many toys did Ben have at first?
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I will solve the problem using backward solution method.
To make the solution totally clear, I will present / (will re-tell) the problem's description in steps.
1. At the start, the total number of toys was 4850.
2. Ben gave 3/7 of his toys to Gilian.
3. Gilian then gave 1/3 of her toys to Ben.
4. After that, the ratio of Gilian's toys to Ben toys was 2:3.
At this point, I start my solution.
Notice that, althought Gilian and Ben exchanged toys, the total number of toys remained 4850, with no change.
So, at the final step 4, there were totaly 4850 toys in the ratio Gilian to Ben as 2:3.
It means, there were 5 equal parts of toys, each part counted 4850/5 = 970 toys,
and Gilian had 2 such parts, or 2*970 = 1940 toys, while Ben had 3 such parts, or 3*970 = 2910 toys.
In particular, we just know the ANSWER to question (a): Gilian had 1940 toys at the end.
Next, the last action that Gilian did was giving 1/3 of her toys to Ben.
HENCE, her final number of toys, 1940, is 2/3 of what she had before this giving.
So, we conclude that before giving to Ben, Gilian had (3/2)*1940 = 2910 toys.
Again, immediately before step 3, Gilian had 2910 toys.
Hence, immediately before step 3, Ben had the rest 4850 - 2910 = 1940 toys.
Thus we analysed the final stage and then restored from the condition, that immediately before step 3,
Gilian had 2910 toys, while Ben had 1940 toys.
Next, moving back, we know that after step 2, Ben had 1940 toys; Gilian had 2910 toys.
In other words, after giving Gilian 3/7 of his toys at the step 2, Ben left with 1940 toys; it is 4/7 what he had before his giving.
HENCE, before this giving, Ben had 7/4*1940 = 3395 toys and Gilian had the rest 4850-3395 = 1455 toys.
Again, immediately before step 2, Ben had 3395 toys anad Gilian had the rest 1455 toys.
It gives the ANSWER to question (a): at first, Ben had 3395 toys.
Completed and solved.
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Yes, I solved the problem using the backward solution method,
and it required very accurate logic and accurate presentation.
Answer by 54929(12)  (Show Source):
You can put this solution on YOUR website! a) Since the ratio of toys was 2:3, total toys are
4850
Hence 4850 * 2/2+3 = 1940
the answer is 1940 toys
b) Assuming Ben had x toys at first
Gillian had y toys at first
{ (1-3/7)x + 1/3(3/7x + y) = 4850 * 3/5
{ (3/7x + y) (1 - 1/3) = 1940
{ 5/7x + 1/3y = 2910 => { x = 3395
{ 2/7x + 2/3y = 1940 { y = 1455
Ben had 3395 toys.
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