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?

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.