Is My Slope-Intercept Equation for Farmer Jack's Milk Prices Correct?

[bayswomen]

I need some help for a math problem. I don't know if my equation is right or not. Thanks so much for any help!
P:
Farmer Jack sells one-gallon cartons of milk (4 quarts) for $3.09 each and half-gallon cartons for $1.65 each. Assume that the number of cents you pay for a carton of milk varies linearly with the number of quarts the carton holds.

a. Write the paticular equation expressing price in terms of quarts.
b. If Farmer Jack sold 3-gallon cartons, what would your equation to predict the price be?
c. The actual prices for pint cartons (1/2 quart) and one quart cartons. Do these prices fit your mathematical model? If not, are they higher than predicted, or lower?

So, for my equation:
if P= number of cents, n=number of quarts, and k= a constant
p/n=k

How do I put that in slope intercept and standard form? Thanks again for any help!

 

[codyg1985]

Hello,

If your current equation is k = \frac{p}{n}, then you would want to solve for the variable that is dependant on the other one. That is, solve for the variable that you end up with when you put something into the equation.

To put that equation in standard form, take your equation in slope-intercept form and move everything to one side of the equation, leaving zero on one side and everything else on the other side. Make sure that what you get does not have a negative sign at the beginning.

 

[HallsofIvy]

But that won't work: If it were p= kn (price is k times number of quarts) then the price of 4 quarts (one gallon) would be exactly twice the price of 2 quarts (a half-gallon). That not true. 2(1.65)= 3.30, not 3.09 as we are told.

a. Write the paticular equation expressing price in terms of quarts.

Since the problem says varies linearly (NOT neccessarily a "direct proportion") the formula must be the more general linear equation p= kn+ b where b is some "starting value". You KNOW that when n= 2, p= 1.65 so 1.65= k(2)+ b and that when n= 4,
p= 3.09 so 3.09= k(4)+ b. Solve for k and b. (Subtracting one equation from the other will immediately eliminate b.)

b. If Farmer Jack sold 3-gallon cartons, what would your equation to predict the price be?

Now that you have found k and b and know what the equation is, set n= 3 and calculate p.

c. The actual prices for pint cartons (1/2 quart) and one quart cartons. Do these prices fit your mathematical model? If not, are they higher than predicted, or lower?

There's something missing! Your first sentence doesn't have a "verb phrase"
"The actual prices for pint cartons (1/2 quart) and one quart cartons"- ARE WHAT?
Put n= 1/2 and 1 in your equation to find the "formula" value for the prices and compare them to the values you are given (but didn't tell us!).