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

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In summary, Farmer Jack sells one-gallon cartons of milk (4 quarts) for $3.09 each and half-gallon cartons for $1.65 each. Whenever he sells a carton that holds more than 3 quarts, he charges an additional cent. If he sold 3-gallon cartons, the equation to predict the price would be k= \frac{p}{n} and the price would be $3.65 per quart.
  • #1
bayswomen
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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!
 
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  • #2
Hello,

If your current equation is [tex]k = \frac{p}{n}[/tex], 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.
 
  • #3
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!).
 

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

1. What is the slope-intercept form of an equation?

The slope-intercept form of an equation is y = mx + b, where m represents the slope of the line and b represents the y-intercept, or the point where the line crosses the y-axis.

2. How do you find the slope and y-intercept of a line using the slope-intercept form?

The slope of a line can be found by looking at the coefficient of x in the equation, which represents the ratio of the change in y to the change in x. The y-intercept can be found by looking at the constant term, b, which is the point where the line crosses the y-axis.

3. Can any linear equation be written in slope-intercept form?

Yes, any linear equation can be written in slope-intercept form. If an equation is not already in this form, it can be rearranged to match the format y = mx + b by solving for y.

4. How can slope-intercept form be used to graph a linear equation?

To graph a linear equation in slope-intercept form, plot the y-intercept on the y-axis and then use the slope to find additional points on the line. The slope tells you how many units to move up or down and left or right to find these points.

5. Can slope-intercept form be used to solve systems of equations?

Yes, slope-intercept form can be used to solve a system of equations by setting the equations equal to each other and then solving for the point of intersection, which represents the solution to the system. This can be done by graphing the equations or using algebraic methods such as substitution or elimination.

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