Question

An omelette costs $1.50 more than Mario's order of pancakes. After treating his family to breakfast, Mario is sure that 4 omelette and 3 orders of pancakes cost more than $25 but not more than $40, including tax of 7% and a tip of $3.50. In what price range is an order of pancakes?

Answer 1

The other answer here, by Nicholasrichar, has the correct answers,
but it's a pain to follow through step-by-step because of the formatting
problem.  Here's my solution, leading to the same answers:

P = cost of pancakes
cost of omeletto, = P+1.50

4 omelettes = 4P + 6
3 pancakes = 3P

Total cost of food = 7P + 6
After 7% tax         = 1.07(7P + 6)
After tip                = 1.07(7P + 6) + 3.50

Eliminate parentheses:  1.07(7P) + 1.07(6) + 3.50 =
                                        7.49P    +    6.42  + 3.50  = 

Total cost of breakfast:        7.49P + 9.92 .

Having a "range" between $25 and $40 is really two inequalities:

First inequality:    $25 < 7.49P + 9.92

Subtract 9.92 from each side:  15.08 < 7.49P

Divide each side by 7.49:          $2.013 < P

An order of pancakes costs more than $2.01 .


Second inequality:    7.49P + 9.92 < $40

Subtract  9.92 from each side:  7.49P < 30.08

Divide each side by  7.49 :              P < $4.016

An order of pancakes costs less than $4.02.

The price range of an order of pancakes is   $2.01 < Pancakes < $4.02 .

Answer 2

Why isn't my formatting working :/ So, if an order of pancakes cost x, then an omelette costs x+$1.50 ... Making the total order = 4*(x+$1.50) for omelettes + 3*x for pancakes. = 4x + $6.00 + 3x = 7x + $6.00 So, the limits: 25 = 1.07 * (7x + 6) + 3.50 40 = 1.07 * (7x + 6) + 3.50 25 = 1.07 * (7x + 6) + 3.50 x = (21.50/1.07 - 6) / 7 x = $2.01 40 = 1.07 * (7x + 6) + 3.50 x = (36.50/1.07 - 6) / 7 x = $4.01 (I rounded down in this case) Substituted back in and they work. That's how I'd do it. :/