Question
A box contained 50¢ coins and 20¢ coins in the ratio 2:3. When I took out four 50¢, exchanged them for 20¢ coins, and put then put the money back into the box, the ratio became 2:7. Find the sum of money in the box.
Answer
Two different ways to solve this problem
5 comments:
Hi, there
Thanks so much for answering my question...and for 2 methods - the 2nd method's only applicable if the value of the coins added/subtracted are equal.
I have a query for the 1st method
3(u+2) - this is because the difference in coins added is 6.
So 6 divided by 3 units (original) is 2 units, hence u +2....
Is this correct reasoning?
You have to compare the bar-1 (first model) with bar-1 (second model). The # of 50cent coins in first model equals to 2u+4, hence 1 unit in first model equals u+2. Hope it clears your doubt.
Thanks for your quick reply...actually, you are comparing the 20 cent coins
(After less coins added)
7 u - 10 - this I understand
I can't get the 3(u+2) ...besides it's 2u-4 for 20 cent coins, not 2u +4, right? Apologies for not being able to get it
Anyway, could you assist me with this dist/speed sum?
Dist betw Town X and Y = 100km
At 0700, Sam left Town X and cycled towards Y.
Ann left Town X and cycled towards Y at 0730.
Ann's cycling speed was 4 km/h faster than Samuel. At 1000, Ann caught up with Samuel. When Ann was 28 km from town Y, she stopped to wait for Samuel.
(a) How far was Samuel from Ann when she stopped to wait for him?
(b) How many minutes did Ann wait for Samuel?
Once you get the answer for u, you can use the first model to work out the total. One block=u+2, so 50 cents x 2 x (u+2) and 20 cents x 3 x (u+2)
In the top model, it is (u + u + four 50 cents) coins. So one block in the top model will be (u+2) 50-cents coins
In order to understand it, you need to compare the two models. That's why alignment of the two is important
Thanks again for your patience in explaining your models !! I understand them now :)
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