Pens and pencils.?

Question

A bookstore manager plans to spend $60 on pens and 30 cents each and pencils at 10 cents each. The equation 0.10x + 0.30y = 60 can be used to model this situation.
a) What do x and y represent?
b) Graph the equation
c) Write the equation in slope-intercept form
d) What is the slope of the line?
e) What does the slope tel you?

Answer 1

a) x = number of pencils, y = number of pens

b) straight line

c) y = (-1/3)x + 200

d) -1/3

e) For each pen added, 3 pencils are removed

Answer 2

SInce pencils cost $0.10, x represents teh number of pencils and hence y represents the number of pens.

b does not lend itself well to text based answers.

Slope intercept form is y = mx + b where m is slope and b is y intercept.

60 = 0.1*x + 0.3*y --> divide by 0.3
200 = 1/3 x + y --> subtract 1/3 x from both sides

y = 200 - 1/3 x

Slope is -1/3 amd it says that for every 3 pencils the manager buys, he or she can buy one less pen. Basically this equation makes the number of pens purchased a function of the number of pencils purchased.

Answer 3

a) x represents pencils because it's like $0.10 per pencil times how many pencils equals a sum of money. So y must represent pens

b)The easiest way to do this would be to solve for y and get your equation in the form:

y = mx + b

Doing this, I get:

y =200 - 0.33333x

Now, just plug in something like 0 to 100 for x and plot your results on a graph.

c)This is the slope intercept form (above)

d)the slope is m: -0.3333 or (-1/3)

e)It tells you rise over run. In this case, we will go down one unit for every 3 we go to the right.

Answer 4

a) x represents pencils and y represents pens

b) You will have to graph it by plugging in numbers.

c) 0.10x + 0.30y = 60
0.30y = -0.10x + 60
y = -0.333x + 200

d) -0.333

e) that as the number of pens increase (y), the number of pencils must decrease.

Answer 5

a). x = number of pens, y = number of pencils
b). I can't graph it on the computer but you could put it in y intercept (y=mx+b) so just get y by itself, y=0.3333x + 200
c). Slope is difference in y over difference in x
d). slope represents change in y over change in x

Answer 6

x is the pencil, y is the pens
b. you have to graph it using the x/y ints
x int = 600 y int=200
c. 0.30y=-10x+60
y=-33.33x+200
d. slope is -33.33
e. the more pencils the less the pens