Question

Help pls no clue where to start ​

Answer 1

`P_(rofit)=13x-50\\C_(ost)(70)=960\\P_(rofit)(70)=860\\C_(ost)(100)=1350\\P_(rofit)(100)=1250\\For\ a\ profit\ of\ \$1100\ one\ must\ sell\ 89\ stuffed\ animals.`

Explanation:

I would suggest starting with 1 and working to 4, as it is set up for you like that.

I would start by writing down what you know, then what you need as follows:

`Givens:\\ C_(ost)=13x+50;\\ R_(evenue)=36x;\\P_(rofit)=R_(evenue)-C_(ost);\\ x=N_(umber\ of\ animals)\\`

`Find:\\1.\ Profit\ equation\\2a.\ C_(ost)\ to\ make\ 70\ animals\\2b.\ P_(rofit)\ from\ selling\ 70\ animals\\3a.\ C_(ost)\ to\ make\ 100\ animals\\3b.\ P_(rofit)\ from\ selling\ 100\ animals\\4.\ N_(umber)\ of\ animals\ needed\ to\ produce\ P_(rofit)\ of\ \$1100`

Now you can read it easier. Given that Profit is Revenue minus Cost, plug the equations for Cost and Revenue into the Profit equation as follows:

`P_(rofit)=36x-(13x+50)\\NOTE:\ Do\ NOT\ forget\ to\ put\ the\ C_(ost)\ equation\ in\ parenthesis\ as\ you\ \\must\ subtract\ the\ entire\ C_(ost).\\\\Distribute\ the\ negative:\ P_(rofit)=36x-13x-50\\Combine\ like\ terms:\ P_(rofit)=13x-50`

With the Profit equation, it is now easier to solve 2b, 3b, and 4.

`C_(ost)\ for\ 70: C_(ost)=13(70)+50=(700+210)+50\\NOTE:\ I\ used\ the\ fact\ that\ 13*70=(10+3)*70=10*70+3*70\\C_(ost)=910+50=960\\This\ could\ also\ be\ written\ more\ clearly\ as\ C_(ost)(70)=960\\\\P_(rofit)(70) = 13(70)-50\\P_(rofit)(70)=(700+210)-50\\P_(rofit)(70)=910-50\\P_(rofit)(70)=860\\\\C_(ost)(100)=13(100)+50\\C_(ost)(100)=(1300)+50\\C_(ost)(100)=1350\\\\P_(rofit)(100)=13(100)-50\\P_(rofit)(100)=(1300)-50\\P_(rofit)(100)=1250\\`

Problem 4 will involve using the (now) known amount for profit, $1100 to find the unknown number of animals. This will involve a little bit more "algebra" compared to the prior questions.

`P_(rofit)(x)=1100=13x-50\\1100=13x-50\\`

Because 13x - 50 is 1100, 13x will be 1100 + 50, just as

`5*2+10 = 20\\5*2=20-10\\`

So, add 50 to both sides:

`1100+50=13x-50+50\\1150=13x\\`

Because 13x is 1150, x will be 1150÷13, just as

`5*2=10\\5=(10)/(2)`

So, divide 13 from both sides:

`(1150)/(13)=(13x)/(13)\\\\(1150)/(13)=x`

Because 1150/13 is not an integer, use a calculator, or simplify the improper fraction to obtain...

x=88.5 (Approximately)

But, because you cannot sell half an animal, you would have to sell 89 in order to profit $1100, for bonus points, what is the actual profit accrued by selling 89 animals?