no clue: sales, costs, revenues; linear patterns; etc.

[bookgrl08]

1)Find the number of sales necessary to break even for the cost C of x units and the revenue R obtained by selling x units if C=1000x+75000 and R=1250x.

*i think you take C & R and set them equal to eachother and solve like you would when looking for points of intersections of lines...

2)A business had annual sales of $110,000 in 1992 and $224,000 in 1995. Assuming that the annual increase in sales followed by a linear pattern, what were the sales in 1994?

*i have absolutely no clue how to do this one... but i'm pretty sure its a rate of change problem..

3) A business had annual retail sales of $124,000 in 1992 and $211,000 in 1995. Assuming that the annual increase in sales follows a linear pattern:
a) calculate the average rate of change of the sales per year.
b) write a linear equation giving sales S in terms of the year t where t=0 corresponds to 1992.
c) use the linear equation to predict retail sales in 2000.

if you can help walk me through these, showing the steps, that'd be great... they're extra pratice... things that i'm having a hard time understanding...

thanks

 

[stapel]

1)Find the number of sales necessary to break even for the cost C of x units and the revenue R obtained by selling x units if C=1000x+75000 and R=1250x.

Hint: Look up the definition of "break-even point". This will tell you the equation to create and solve.

2)A business had annual sales of $110,000 in 1992 and $224,000 in 1995. Assuming that the annual increase in sales followed by a linear pattern, what were the sales in 1994?

They've given you two points in the form (year, sales). Since they started counting in 1992, make that year 0, so "t = 0" means "1992". Then larger t-values will indicate "number of years after 1992".

Once you have your points, find the slope of the line through them. Then use whatever formula they gave you to find the line equation (the "linear pattern").

If t = 0 is 1992, what t-value is 1994? Evaluate your function, y = mt + b, for that t-value to find the sales in 1994.

3) A business had annual retail sales of $124,000 in 1992 and $211,000 in 1995. Assuming that the annual increase in sales follows a linear pattern:
a) calculate the average rate of change of the sales per year.

This is the slope.

b) write a linear equation giving sales S in terms of the year t where t=0 corresponds to 1992.

This is the line equation.

c) use the linear equation to predict retail sales in 2000.

This is the evaluation part.

If you get stuck, please reply showing how far you have gotten. Thank you!

Eliz.