Question

Johnny wants to start making and selling surfboards. His costs are the large sum of money that includes his initial investment and the cost of materials for each surfboard. He has already planned how much he is going to sell his surfboards for. Explain how Johnny can set up a system of equations to predict when he will start to make a profit.

Answer 1

hopefully i could get an example of a system of equations that would apply to this

Answer 2

"Making and Selling" So you can set-up a system for that and by using it you can solve for when they will be equal so that after that point he will start to see a profit or loss.

Answer 3

i just need an example equation for the world problem

Answer 4

You can easily come up for the equation for selling the surfboards. Each time he sells a surfboard he makes an amount. So if we say that a constant dollar amount is used and the profit Y is based on how much of those he sells x then
Profit = Constant times Amount sold

Answer 5

Or Y = (some number) times X

Answer 6

im guessing the investment value doesn't get a variable then?

Answer 7

As for making the surfboards you can see that he has an a large initial investment plus the cost of materials per surfboard so
Cost of making = Initial investment +(materials price) times (each surfboard)

Answer 8

Correct the initial investment is a constant dollar amount so
Y = (Initial Investment)+(cost of making) times x

Answer 9

If you make values for the initial investment, cost of materials, and how much he sells each surfboard for you can use when the cost and profit are the same or better known as when our Y values are equal and solve for x the amount he will need to make and sell to get there.

Answer 10

So lets say the investment value was 4500 and each board costed 100 to make and he sold them for 500 each

Answer 11

You just plug them in.

Answer 12

But the problem has to be two equations
my teacher said

Answer 13

You do have 2 equations.

Answer 14

Cost = Initial Investment +(material cost) times x

Profit = (How much he sells board for) times x

In this case x = how many made and how many solve

Answer 15

If we set variables to our values,
Cost = Y
Profit = Y (They are both why because we want to find when they are equal to each other)

Answer 16

Then we have the cost to make them as\[Y = 4500 + 100X\]
And the profit of each solve as:\[Y =500X\]

Based on the information you have given

Answer 17

Setting when Both our Ys are equal means that we have the same amount of profit and cost so that Johnny breaks even and from that we can find X how many have to be made and sold.

Answer 18

When Cost = Profit
\[Y=Y\]
or
\[4500+100X=500X\]

Does this make sense?

Answer 19

yeah i seen a messed up example and it messed with my logic
im currently working it out hold up

Answer 20

Oh alright, as long as you understand it now. Take your time.

Answer 21

disregard the value of how much he was gonna sell each of them for

Answer 22

it saids in the question that he already knows how much he was gonna sell them for

Answer 23

so what would i do now

Answer 24

So what do you mean by that? 500 is not the amount he is going to sell them for?

Answer 25

i wasn't suppose to include that sorry

Answer 26

You can not solve the problem for X without knowing the value of how much he sells them for

Answer 27

Because we will have Three variables and only 2 equations.

Answer 28

sooooooooo Y=4500+100x whats the second equation

Answer 29

If we do not know the dollar value for each surfboard we will need to set a variable for that and lets call it Z so that our new equation for that is:
\[Y = ZX\]

Answer 30

Where Z = a constant dollar value for the sale of each surfboard

Answer 31

ok

Answer 32

still need help

Answer 33

What's up?

Answer 34

How may I help?

Answer 35

Y=4500+100X
Y=500X
didn't solve anything

Answer 36

That is if Johnny sells the surfboards for 500 dollars a piece. You would need to set when the profit is equal to the cost or as explained Y=Y and solve for the amount he has to make and sell or "X" and that number has to be rounded to the nearest integer if it is a decimal because Johnny can not make a decimal of a surfboard.

Answer 37

\[4500+100X=500X\]
You can use algebra to solve for X. Subtract 100X from both sides and then divide both sides by the new number next to the X to get the value of x

Answer 38

4500+100x=500
-100 -100
4400/400?

Answer 39

Not quite. The 100 has an X next to it so you will need to remember about combining like terms.

Answer 40

oooooooh

Answer 41

\[4500+100X = 500X\]
If we subtract 100X from both sides:\[4500+100X-100X= 500X- 100X\]

Answer 42

You can see that the left side both 100X will cancel out and the right side we combine like terms to get:
\[4500 = 400X\] Now you can divide both sides by only 400 to get X by itself.

Answer 43

what whould you do to implement the amount he sold in the equation

Answer 44

When I have the value of X, I would plug the unrounded value into the equation labeled profit and solve for Y the amount of profit needed to break even and from there I know any surfboard sold after that point will start to make profit.

Answer 45

alright got it now thanks

Answer 46

My pleasure.