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December 1st, 2017, 10:10 AM   #1
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Simple question about rent split

If the rent for a house is £895 per month and is being rented by 2 people. One is accepted to pay £20 more per week, what is going to be monthly payment for each of those people?

Is it going to be £407.50 for one and £487.50 for the other OR £367.50 and £527.50 for the other?

I'm pretty sure it's the first statement.

The second has been calculated by my mate who is arguing that £895/2 = 447.50 and £447.50 - £80 = £367.50 and 447.50 + £50 = £527.50.

My logic is £895 - 80 = £815 £815 / 2 = £407.50 £407.50 + £80 = £487.50 for one and the rest for the other.

Last edited by lazio; December 1st, 2017 at 10:14 AM.
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December 1st, 2017, 10:33 AM   #2
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First $\displaystyle X+Y=895$ and $\displaystyle X=Y+20\cdot 4=Y+80$
$\displaystyle 2Y+80=895$
$\displaystyle Y=407.5$
The first statement is true
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December 1st, 2017, 10:41 AM   #3
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That's exactly what I mean. How can I in the simplest way explain this? My mate doesn't understand algebra, I assume. He doesn't understand the fact that you shouldn't divide the whole amount and -80 from one amount and +80 from the other but -40 and +40 so the gap could equal £80.

Last edited by skipjack; December 1st, 2017 at 11:18 AM.
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December 1st, 2017, 11:26 AM   #4
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Both methods can be made to work, but I would first question the assumption that you both make that a month contains 4 weeks.
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December 1st, 2017, 03:38 PM   #5
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If you work from the premise that a month has 4 weeks, there is a simple way to explain it.

An even split would be $\dfrac{895}{2} = 447.5.$

No difficulty there.

Now compute $447.5 + 40 = 487.5.$ Straight forward, no algebra.

And compute $447.5 - 40 = 407.5.$

So if you pay 487.5 and your mate pays 407.5 that sums to

$487.5 + 407.5 = 895.0.$ Simple arithmetic.

And what is the difference in the rent paid?

$487.5 - 407.5 = 80 = 4 \times 20.$ Simple arithmetic.

If you ignore how you got the answer and just explain why the answer pays the rent and has you paying 80£ more, all you need is very basic arithmetic.

So this is the correct answer if what your agreement was REALLY involved a differential of 80 quid a month. But it is not correct if your agreement REALLY involved a differential of 20 quid a week because the answer calculated assumes that there are only 48 weeks in the year when in fact there are just about exactly 52. If the latter is the case, then here is what is called for.

Your monthly payment $= 490.83.$

Your mate's monthly payment $= 895 - 490.83 = 404.17.$

Now you are paying together $ 490.83 + 404.17 = 895.$

And you are paying $490.83 - 404.17 = 86.66$ more each month.

That makes sense because there are a bit more than 4 weeks in the average month. Now let's how it works out over a year.

Annually, you pay $12 \times 490.83 = 5889.96$

Annually, your mate pays $12 \times 404.17= 4850.04.$

Notice the sum totals $10740 = 12 \times 895.$

In total, you pay $5889.06 - 4850.04 = 1039.02$ more in a year.

And $52 \times 20 = 1040.$

At the end of the year you owe him a quid.
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