I saw this on discord and I feel like an idiot but I’m so confused.
*”Question for you guys If I borrow $50 from my mom and $50 from my dad to purchase an object worth $97. Since I would have $3 change I would give one to my mom and one to my dad and keep one my self
So I still owe my mom $49 and my dad $49 that means I owe $98 counting the one I have makes is $99 where did the other $1 go?”*
In: Mathematics
You are mixing up two different hings: what you owe your parents and what you have.
In the end you have an item worth $97 and $1 in money, but you also have $49 + $49 in debts.
$97
$1
-$49
-$49
—-
$0
You started out with zero assets, zero debts and zero money. Then you had zero assets, $100 in debts and $100 in cash and then you had $97 in assets $100 in debts and $3 in cash and in the end you had $ 97 in assets, $98 in debts and $1 in cash.
| start | getting a loan | buying the item|partial repayment of debt
—|—:|—-:|—-:|—:
Assets | $0 | $0 | $97| $97
Cash | $0 | $100 | $3| $1
Debt | $0 | -$100 | -$100| -$98
||||
Total| $0|$0|$0|$0|
It’s simply a trick where they try to confuse you with how much money you get back. So you have 3 dollars back from your purchase. That 3 dollars has nothing to do with your debt though. Your total debt is 100 dollars and you payback 2 of it so you still owe 98. The dollar you have left is the difference between the price of the toy and the debt. I don’t know if explaining it with letters will clear it up or not, but I’m quite fond of turning word problems into algebra as it makes it sensible.
Debt to mom=m
Debt to dad=d
Price of toy=p
Change from purchase=c
Total debt= x
So the first bit goes like this
(m+d)-p=c
Then the next step is this
(m+d)-(c-1)=x
Then they ask the question
X+1=/=m+d
Or why doesn’t total debt plus one equal the original debt. The reason is because the two equations aren’t related. If you use the system of equations from above you can see that:
X+1=(m+d)-(c-1)+1
Because that’s the established relationship between x, m, d, and c.
The reason it’s confusing is because 3 + 97=100. So your brain is looking for a total of 100 when what youre really looking for is 98-1=97 the purchase price.
Tl;dr 49+49=98 and 98-1 is 97 which is the purchase price and how much the debt would equal if you paid back all 3 dollars. So 98 is the debt remaining after you pay the 2 dollars, so you would subtract the other dollar to get the price not add it back to get 100. It’s like a math tongue twister is why you’re struggling with it.
Everything in that sentence is logically correct until “counting the one I have makes is $99”. Why would you add the amount you owe with the amount you have? If I have 1,000 and I owe you 500, does the sum of 1500 have any significance at all?
It is poorly written. Okay here we go.
The problem says that Dude borrows a total of $100 to purchase a $97 item. What he then has are two $50 debts. He spends $97, leaving him with $3. He puts $1 towards each debt, leaving him with two $49 debts and a dollar which he is keeping.
What he actually has is a $97 dollar item, a dollar in hand, and two $49 dollar debts. The way the problem is written leads you to assume that all those things should add up to one hundred, like this:
49+49+1=100
That is of course incorrect. What it should look like is kind of a before and after on each side of the equation. His loans on one side and the purchase price and change on the other. Like so:
$50+$50=$97+$3
The change then being distributed to his parents and himself.
You owe $98, and you have $1.
You can’t add what you have to what you owe without keeping track of the sign.
Debts are usually expressed as negative, so you HAVE -$98 and you HAVE $1, so if you wanted to add that up, the total would be -98 + 1 = -97. Debt of 97 and object worth 97.
I don’t understand. What exactly is “the problem”?
To me it looks like you’re just adding together random numbers and then wondering why they’re not equal to $100.
The $98 dollars you owe includes the $97 you paid, and the $1 in your hand. So why are you adding the $98 you owe and the $1 you have together? The former includes the latter.
This problem is only difficult because it’s worded like a spider web. Anyways, let’s map this out:
You have $3 in change. After giving $1 back to each of your parents, you’ve returned $2 total. The money you owe is equal to the price minus the amount you’ve already returned, so $100-$2=$98. The $1 is useless for finding out how much you owe, since it’s not the price or the money you’ve returned, so it’s just a word play.
You owe $98 total. And you have $98 worth of stuff ($97 object plus $1). 98 including the one you have is just 98, not 99.
“Counting the one i have” doesn’t make any sense for the problem. It doesn’t make sense to count the $1 he has as something he/she owes their parents. And the $100 value is also completely irrelevant so the “other dollar” doesn’t matter
In short, this is nonsense 🙂
It’s a misdirection. You do owe $98 total, having paid $2 back. That third dollar you kept, you down’t owe yourself.
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