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spesh 1/2 question

(1/1)

a weaponized ikea chair:
Hey,

Here's the question:

A father distributes $96 to his 3 children according to the following instructions: the middle child gets $12 less than the oldest, and the youngest receives one third as much as the middle child. How much does each receive?

My problem is that my solution works (at least I think it does) but the textbook says otherwise.

I got:

OLDER CHILD: $37.20
MIDDLE CHILD: $25.20
YOUNGEST: $33.60

Textbook:

OLDEST: $48
MIDDLE CHILD: $36
YOUNGEST: $12

Now, I'm not an idiot right, I get that one third as much means, well, one third as much, right? But when I used that logic for a similar question I get the wrong answer. Here was the other question:

A biathlon event involves running and cycling. kim can cycle 30km/h faster than she can run. if kim spends 48 minutes running and a third as much time again cycling in and event that covers a total distance of 60 km, how fast can she run?

If you take her cycling as 16 minutes, which is a third of 48, you get the wrong answer. So I am confused by this double standard unless I'm missing some slight grammar rule or something.

1729:
The idea is, like, if you get more money, you have more money, but if you run faster, you spend less time, it's opposites.

--- Quote from: a weaponized ikea chair on July 09, 2020, 06:03:16 pm ---A father distributes $96 to his 3 children according to the following instructions: the middle child gets $12 less than the oldest, and the youngest receives one third as much as the middle child. How much does each receive?

--- End quote ---
This makes me think that you add up the 3 children's moneys will equal 36, so a + b + c = 36

--- Quote from: a weaponized ikea chair on July 09, 2020, 06:03:16 pm ---the middle child gets $12 less than the oldest

--- End quote ---
If we consider the first number to be the oldest child (lets say x represents the oldest child's moneys), then the middle child or the second number would be (x-12)

--- Quote from: a weaponized ikea chair on July 09, 2020, 06:03:16 pm ---the youngest receives one third as much as the middle child

--- End quote ---
Since the middle child receives (x-12) and the youngest receives a third of this, the youngest would receive (1/3)(x-12)

Can you make an equation with this?
equation

a weaponized ikea chair:

--- Quote from: 1729 on July 09, 2020, 06:36:21 pm ---The idea is, like, if you get more money, you have more money, but if you run faster, you spend less time, it's opposites.

--- End quote ---
When she cycles, which she does faster than running, she takes more time.

a weaponized ikea chair:
wait nvm get it now

thanks for your help

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