# show that R = 14 400 + 840x - 30x^2

#### bumblebee123

##### Junior Member
I can't understand this question for some reason! can anyone help me to figure it out?

question:

The owner of 40 apartments knows that, at a rent of $360 per week, all apartments will be occupied. For each increase in rent of$30 per week, one fewer apartment will be occupied. He increases the rent from $360 per week to$(360 + 30x ) per week. After this increase, the total income he receives is $R per week Show that R = 14 400 + 840x - 30x^2 any help would be really appreciated! #### pka ##### Elite Member question: The owner of 40 apartments knows that, at a rent of$360 per week, all apartments will be occupied. For each increase in rent of $30 per week, one fewer apartment will be occupied. He increases the rent from$360 per week to $(360 + 30x ) per week. After this increase, the total income he receives is$R per week
Show that R = 14 400 + 840x - 30x^2
Have a look here.

#### Jomo

##### Elite Member
Think about what x means. It represents the number of $30 increases in rent, Well for each$30 increase in rent, one less apartment is rented (from 40).
Now you have the rent that is being charged and now need the number of apartments that are rented. Since the rent is increased by $30 x-times then there must be 40-x apartments rented. The total revenue taken in per week will be$(360+30x)(40-x). Now multiply this out and see what you get!

#### bumblebee123

##### Junior Member
Think about what x means. It represents the number of $30 increases in rent, Well for each$30 increase in rent, one less apartment is rented (from 40).
Now you have the rent that is being charged and now need the number of apartments that are rented. Since the rent is increased by $30 x-times then there must be 40-x apartments rented. The total revenue taken in per week will be$(360+30x)(40-x). Now multiply this out and see what you get!
R = 14 400 + 840x - 30x^2

ah! thank you so much, that's what I was getting confused about- I couldn't figure out what x meant. This makes sense now haha ( you're always so helpful! )

#### Jomo

##### Elite Member
ah! thank you so much, that's what I was getting confused about- I couldn't figure out what x meant. This makes sense now haha ( you're always so helpful! )
I hope that you put all your energy into thinking what x meant as you can't do this type of problem w/o knowing what the variable meant.

Thanks for the complement. I hope that my boss can finally give me a real raise. My boss only agrees to give me a percent increase which literally amounts to no raise at all. Ah well, at I least I am having fun and helping students (not necessarily in that order as students always come first)