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Question

Andy and Bruce had some money. Andy had 50% more money than Bruce. After Andy gave Bruce $77, Bruce had 25% more money than Andy.

(a) How much money did they have in total?

(b) How much money must Bruce then give to Andy so that Andy will have 50% more money than Bruce? 

Answer

(a)
Andy : 1.5u – 77
Bruce : 1u + 77

1u + 77 ——- (1.5u – 77) x 1.25 = 1.875u – 96.25
1u ——- (77 + 96.25)/(1.875 – 1) = 198
2.5u ——- 495

(b) (Return the $77)
495/5 = 99

99 x 2 = 198
198 + 77 – 198 = 77
or
99 x 3 = 297
297 – (1.5 x 198 – 77) = 77

Ans : (a) $495; (b) $77.

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At first, Andy had 50% more money than Bruce.

That was no longer the case after Andy gave Bruce $77.

Now part (b) wants us to find out how much Bruce should give to Andy so that Andy again had 50% more money than Bruce.

So isn’t it just return the $77 to Andy??? Or am I missing something??

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Thanks for the answer. You’re right about part b, maybe there’s an error somewhere, not sure. Let me go check.

As for part a, how do you derive 9u and 5u for the model drawings?

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This is something my kids were taught and known to them as unit equalisation.

Important thing to note is that there was no loss of money in the before and after model. All movements of money were strictly between the 2 boys.

So in the before model, you get 5 boxes (B had 2, A had 1.5 × 2 = 3)

In the after model, there were 9 boxes (A had 4, B had 1.25 × 4 = 5)

Since the 5 boxes before represents the same amount of money as 9 boxes after, we take the LCM of 5 and 9 -> 45

So the 5 before boxes were 9u each for a total of 45u

and the 9 after boxes were 5u each also for a total of 45u

Hope this is clear?

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Need some time to digest it. Thank you.

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