Question flaw?
My answer
Benedict $90
Calvin $290
... and there spend for 2.5 days... look weird.
Need to wait for Eric answer.

Let number of day spend = u
Case 1
Benedict spend 36 x u = 36u
This is money Benedict have
Calvin spend 12 x u = 12u + 260

Case 2
Benedict spend 12 x 3u =36u spend all his money.
Calvin spend 36 x 3u = 108u + 20

From here, Calvin money
12u + 260 = 108u +20
96u = 240
u = 2.5
.
.
.
Weird...

Not so sure. There should be a solution for this, but then I am wondering how. Basically in the scenario where Benedict spends $12 per day, the number of days taken will be 3 times the number of days in the other scenario.

1. Calvin spends $12 per day, Benedict spends $36 per day. Calvin has $260 left when Benedict runs out of money.

2. Calvin spends $36 per day, Benedict spends $12 per day. Calvin has $20 left when Benedict runs out of money.

Clearly the number of days taken in the second scenario (when Benedict spends $12 per day) is three times the number of days taken in the first scenario (when Benedict spends $36 per day).

We have no idea how many days this actually is, so we let the number of days in the first scenario be 1 unit and the number of days in the second scenario be 3 units.

Amount of money spent by Calvin in the first scenario is $12 x 1 unit of days = 12 dollar-units in total.

Amount of money spent by Calvin in the second scenario is $36 x 3 units of days = 108 dollar-units in total.

From here, we have

1. Calvin’s starting - 12 dollar-units = $260
2. Calvin’s starting - 108 dollar-units = $20

This means that the extra 96 dollar-units spent in total corresponds to $240 spent.

96 dollar-units = $240
1 dollar-unit = $2.50
12 dollar-units = $30

This means that in the first scenario, Calvin spends $30 when Benedict runs out of money.

Calvin must have had $260 + $30 = $290 at the start.

In this first scenario, number of days it takes Calvin to spend his $30 is 30/12 = 2.5 days. Of course Benedict must have taken the same number of days to spend his money at a rate of $36 per day.

Benedict’s starting money must be $36 x 2.5 = $90.

——————————

Let’s inspect our solution using the other case.

Suppose Calvin starts out with $290 and Benedict starts out with $90.

If Benedict spends $12 per day, he would have taken 90/12 = 7.5 days to run out of money.

Then Calvin would take 7.5 days to spend a total of $36 x 7.5 = $270.

He would have $20 left.

So yes, Calvin has $290 at the start while Benedict has $90 at the start.

The notion of “half a day” here is unusual, considering that at the primary level, “days” (or similar types of questions) are defined as whole numbers and not in halves.

It’s like saying, if I sleep 12 hours a day and stay awake 12 hours a day, I spend $18 while I am awake and “$18 while I am asleep”.

I got $290 as well but I erased it earlier. Updating my previous comment soon.

Hi AC Lim and Eric, FWIW here is the solution from the answer sheet:

B : C
36 x U : 12 x U + 260

B : C
12 x P : 36 x P + 20

36U = 13P 12U = 4P
3U = 1P

12U + 260 = 36P + 20
12U + 240 = 36P
36 - 4 = 32
32P —> 240
1P —> 240/32 = 7.5
Benedict —> 12 x 7.5 = 90
Calvin —> 36 x 7.5 = 270 + 20 = 290

Technically the answer sheet does not make sense because “days” are counted in whole numbers at the primary level.