Question

None.

Answer 1

this is the same kind of question as your previous one, except this time you need to find the equations and solve.

Answer 2

well if you think about any business, you have "income" and you have "expenses" so you need to find an equation for just the income, and you need to find an equation for just the expenses... luckily for us, we are using only one variable, and that is x... for just the amount of boxes... lets start with the easier of the two... can you look at the given information and find an equation for the amount of money she will make for the boxes she sells.

Answer 3

I think you might be misunderstanding the information given.... this person is spending their own money on plain cards for $3 each, then they are painting them, and then turning around and selling them for $5 each.... so the only money they actually make is $5 per card they sell. does that make sense.

Answer 4

okay, no can you take that $5 per card they sell and turn it into an equation in terms of y which would be money, and x which would be the boxes sold

Answer 5

or you can think about it this way
(amount of money she makes) = (cost of the card) x (number of cards sold)

and make that an equation

Answer 6

so as I mentioned above what variable should we use for "amount of money she makes"

Answer 7

its okay... do you understand the concept of

(amount of money made) = (cost per box) times (number of boxes sold)

??

Answer 8

okay... well in our equation the amount of money that is made is y, the cost per box is given to us at $5, and the number of boxes sold is our unknown variable x... so our equation is

y = 5x

if she sold 10 boxes, we would just substitute the 10 in for x and multiply 5 x 10, and get our y.... in this case it would be $50... so by selling 10 boxes she would make $50... if she sold 20 boxes she would make $100...

does this make sense??

Answer 9

okay, so this equation was for our profit or income... it was the amount of made that she will make by selling these boxes...

now we have to do the exact same thing and find an equation using the given information for the expenses, or the amount of money spent to make the boxes.

so use our info left in the question, which was the initial expense of $40 and the cost per box at $3 to make another equation the same way

Answer 10

well we aren't make equations for the boxes... we are just making equations to represent the amount of money that was made and the amount of money that was spent...

we found one already for the amount of money that was made... y = 5x

now we are just trying to find an equation to represent the amount of money that was spent.... and we will do it the same way... except with the amount spent, we are given an initial cost, which is like the y intercept of an equation in slope intercept form...

if you remember slope intercept form is just y = mx+b,
and in this case the b is the $40... and the slope is just 3
so our equation for our cost is
y = 3x + 40

so now we have two equations, and in order to find the intersection of these two equation we set them equal to each other and solve.

so that mean
5x = 3x + 40

then you just solve for x and that will give us our answer, the number of boxes sold.

Answer 11

that is correct... and if you need to visualize it on a graph, just plot the two and find the intersection, which would look something like this...