Posted by Anna on Sunday, December 20, 2009 at 12:04pm.
The Juice Problem. A store sells a 1liter container of
juice for 75¢ and a 2liter container for $1.40. Assume
that the cost varies linearly with the number of liters, and find the slope of the line that shows the relationship.
How many liters would be in a container that cost
$3.35?

Math  MathMate, Sunday, December 20, 2009 at 1:14pm
First find the rule for the cost.
C(1) = 0.75
C(2) = 1.40 (difference = 0.65)
C(3) = 2.05
C(4) = ...
C(x) = mx+0.10
Find m, and then solve for
C(x) = 3.35

Math  Anna, Sunday, December 20, 2009 at 1:48pm
I am still confused, I understand finding the difference and that being 0.65. What I am not sure about is where you wrote c(x)=mx+0.10. I know that the C stands for cost, should the x be a y? I know that m stands for slope but what is the 0.10? I really do not understand linear equations.

Math  MathMate, Sunday, December 20, 2009 at 2:21pm
To express the equation in a more familiar form, it could be
y=mx+b
where b is the yintercept, meaning the value of y when x=0. In this context, it represents a fixed cost, for example, the cost of the container.
We can find b by taking the difference of C(1)m, or 0.750.65 = 0.10.
We therefore end up with
y=0.65x + 0.10
So the question reduces to when y=3.35, solve for x in
3.35=0.65x + 0.10

Math  Anna, Sunday, December 20, 2009 at 2:27pm
Okay that clears it up. Thank you very much for your help.

Math  MathMate, Sunday, December 20, 2009 at 3:52pm
You're welcome!
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