Question

suppose you start a business. You buy a freezer for $200. It costs you $.35 to make a single-scoop ice cream cone. You sell each cone for $1.20. Write and solve a system of equations to find the break-even point for your business. @mathstudent55

Answer 1

You need to find the expenses and the amount coming in and set them equal.
Let's use x as the number of cones needed to break even.

E = Expenses:
You have a fixed expense of $200.
Then you have an expense of $0.35 per cone for x cones.

R = Revenue
The amount coming in is $1.20 per cone for x cones.

Answer 2

ok

Answer 3

How much do the cones cost you if they are $0.35 each and you buy x number of them?

Answer 4

$0.35x

Answer 5

Great.
The total expense, E is:

E = 200 + 0.35x

Now we need the total revenue.
How much are x cones at $1.20 each worth?

Answer 6

200+$1.20x

Answer 7

No. There is no $200 fixed amount associated with the money coming in.
The money coming in is only from the sales of x cones at $1.20 each, so the money coming in is simply $1.20x.

Answer 8

ok

Answer 9

Total expenses:
E = 200 + 0.35x

Total revenue:
R = 1.20x

Answer 10

sorry im not good at math.

Answer 11

The break even point is the number of cones you need to sell to cover all your expenses, but that gives you no profit.

Answer 12

You're doing fine. Just keep paying attention.

Answer 13

That point happens when the expenses equal the revenue.

Answer 14

E = 200 + 0.35x
R = 1.20x

Now we set these two equations equal to each other and solve for x.

Answer 15

ok

Answer 16

200 + 0.35x = 1.20x

Solve for x.

Answer 17

kk

Answer 18

200 + 0.35x = 1.20x

Subtract 0.35x from both sides:

200 = 0.85x

Now divide both sides by 0.85.

x = 235.29

You need to sell 235.29 cones to break even.
Since you can't sell 0.29 of a cone, you need to make 236 cones to break even.

Answer 19

do i add 0.35+1.20x the divide it by 200?.... im sorry if thats wrong