Rent and income

[bigbart100]

Hi,

This one is from the real life.

I applied for an apartment and to meet the criteria:
1. Your net income can't be greater than €53.000 a year
2. Your rent can't be greater than 35% of your income.
3. Rent in first case is €1530 a month and €1550 in second case.

What should be my income to meet both criteria in first case and in second case?

 

[stapel]

This one is from the real life.

I applied for an apartment and to meet the criteria:
1. Your net income can't be greater than €53.000 a year
2. Your rent can't be greater than 35% of your income.
3. Rent in first case is €1530 a month and €1550 in second case.

What should be my income to meet both criteria in first case and in second case?

What do you mean by "in the first case" and "in second case"? Don't both criteria hold? How are you getting a rental price from "net income" "in the first case"?

Please be complete. Thank you!

Eliz.

 

[bigbart100]

What do you mean by "in the first case" and "in second case"? Don't both criteria hold? How are you getting a rental price from "net income" "in the first case"?

Please be complete. Thank you!

Eliz.

First case: rent €1530, second case: rent €1550 - 2 different apartments.

You don't get rental price from net income. Rent is as given.

You must satisfy both criteria in the same time:

1. Net income less than €53.000 a year
2. Rent can't be more than 35% of your income.

What income will hold both criteria?

 

[Steven G]

Well do you earn €53.000 or more per year?
How can we determine if either rent is less than 35% of your income if we don't know your income?

 

[bigbart100]

Ok.

How much can I earn when income treshold is €53000, rent spend can't be more than 35% of income and rent is:

1. €1530
2. € 1550

I don't know how better can I explain that.
If this is still not clear we can delete this.
Thanks

 

[Dr.Peterson]

I applied for an apartment and to meet the criteria:
1. Your net income can't be greater than €53.000 a year
2. Your rent can't be greater than 35% of your income.
3. Rent in first case is €1530 a month and €1550 in second case.

What should be my income to meet both criteria in first case and in second case?

Your mistake was in listing the third item as a criterion. That made this confusing.

How much can I earn when income treshold is €53000, rent spend can't be more than 35% of income and rent is:

1. €1530
2. € 1550

I don't know how better can I explain that.
If this is still not clear we can delete this.
Thanks

Now it is clear.

Let the monthly rent be R, and your income be x.

Write an inequality to represent each criterion, and solve to find a range of values for x (for a given value of R). Don't forget to convert the rent to an annual amount.

Then take each of the rents you mention, and plug them into your answer.

You'll find that one case is impossible. Please show us your work, so we can know where you need help.

(This can also be solved by common sense, rather than algebra.)

 

[stapel]

Ok.

How much can I earn when income treshold is €53000, rent spend can't be more than 35% of income and rent is:

1. €1530
2. € 1550

I don't know how better can I explain that.
If this is still not clear we can delete this.
Thanks

How can anyone compute how much 35% of your income is, if you don't know what your income is?

Are you saying that you are needing to figure out the income of which 35% is equal to (or less than) the listed rents? If so, then do the simple "percent of" computation. (You posted this to "Calculus", so obviously you are well-versed in arithmetic and pre-algebra, which are all that is required if you're simply computing "percent of".)

When you reply, kindly please include recent topics of study, so that we can try to figure out what calculus techniques might be required here. Thank you!

 

[bigbart100]

Sorry for messing here but I wanted second opinion as I am not mathematically strong?

I didn't want to keep to something that maybe based on wrong maths.

€53.000 ÷12mc = €4416.666 X 0.35 = €1545.833

In the case of rent €1550 it is impossible to have income below €53.000 and your rent spent below 35% of that income. Right?

I don't know how to find what income will meet both criteria when rent is €1530.

Somewhere between €52.500 and €5300 but how to find out??

Thanks for your patience ?

 

[stapel]

Sorry for messing here but I wanted second opinion as I am not mathematically strong?

But you're taking (or have studied up through) calculus (at university?), so pre-algebra shouldn't be difficult for you.

I didn't want to keep to something that maybe based on wrong maths.

€53.000 ÷12mc = €4416.666 X 0.35 = €1545.833

I think you mean the following:

Assuming an income of 53,000, we get a monthly income of:

[imath]\qquad 53000 \div 12 = 4416.67[/imath]

Then 35% of that monthly income is:

[imath]\qquad 4416.67 \times 0.35 = 1545.83[/imath]

In the case of rent €1550 it is impossible to have income below €53.000 and your rent spent below 35% of that income. Right?

Yes; given a yearly income of no more than 53,000, it is not possible to be able to pay no more than 35% of that income and also be able to afford the higher rent.

I don't know how to find what income will meet both criteria when rent is €1530.

Somewhere between €52.500 and €5300 but how to find out??

Try following the instructions that were provided in post #6. (If you're needing a refresher for what you learned back in middle school, try a few of the lessons in this listing.) Do the usual basic set-up:

.........(amount) is (some percent) of (total)

You know the rental amount, and you know the percentage. Solve to find the total income. (Hint: Divide.)

 

[Dr.Peterson]

€53.000 ÷12mc = €4416.666 X 0.35 = €1545.833

In the case of rent €1550 it is impossible to have income below €53.000 and your rent spent below 35% of that income. Right?

First, I have to figure out what you did here!

It looks like you divided the maximum annual income, €53.000, by 12, to find the maximum monthly income, €4416.666; then you found 35% of that, which tells you that with that income you could afford no more than €1545.833 monthly rent. Good: so you found that no one can afford the €1550 monthly rent under these conditions.

This is part of the "common sense" approach I suggested was possible.

Now, how can we figure out what income you would need for the €1530 rent. Since you clearly are not up to speed on algebra proper, let's continue with common sense.

What you need to do is to work backward, reversing what you did above. The last thing you did was to multiply the monthly income by 35% to find the rent; so we divide the rent by 35% to find the monthly income: €1530/0.35 = €4371.428. The first thing you did was to divide the annual income by 12 to find the monthly income; so we multiply by 12 to find the annual income, €4371.428*12 = €52457.14.

Since that is less than the maximum allowed, it works.