An omelette costs $1.50 more than Mario's order of pancakes. After treating his family to breakfast, Mario is sure that 4 omelet
te 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
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. :/