Question

Ok, here's a crazy one.
Melinda and JP are selling Lemonade at a stand in her front yard. The linear expression below models her total profit in dollars after h hours.
2
- (6h-5)+4h
3

a. What is her profit after 2 hours? Explain
b. When will her profit be $30? Explain
c. How much does her profit increase each hour? Explain
d. Evaluate the expression for h=0. What does this value mean in the context of the problem?
e. Explain how the answer to part 3 could be calculated mentally just by looking at the expression.
f. Explain how the answer to part 4 could be calculated mentally just

Answer 1

Looks like you could simplify your formula a little
\[\frac{2}{3}(6h- 5)+4h \]
\[= 4h - \frac{10}{3} + 4h\]
\[ = 8h - \frac{10}{3} \]
We could go with decimals, but since the question uses fractions, I would continue to use fractions.

Answer 2

(a) They are giving you 2 hours and asking for profit - this means that they have given you an h value and they want you to find a ... p ??? value. Substitute 2 for h.
\[p = 8(2) - \frac{10}{3} = \; ...\]

(b) They are telling you $30 profit and want you to find hours - this means that they have given you a p value and want you to solve for h. Set the formula equal to 30 and solve for h.
\[30 = 8h - \frac{10}{3} \]

Answer 3

I'm with you so far :o)

Answer 4

ok!

(c) the equation is that of a line, so the are asking you about the slope of the line.

(d) When h = 0, this is at the beginning, before any time has passed. Graphically, it's the y-intercept of the line.

Answer 5

(e) y= mx + b, just look for the number with a variable, that's the slope of the line.
(f) y = mx + b, just look for the number without a variable, that's the y-intercept

Answer 6

Absolutely fabulous! Thank you for your time and efforts in this problem. I really appreciate it!!