spesh 1/2 question

[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.

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?

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

the middle child gets $12 less than the oldest

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)

the youngest receives one third as much as the middle child

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]

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.

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