math
posted by Andrea on .
Olive Oyl sent Popeye and Wimpy out to get spinach and burgers. They bought the following combination: If the square of the number of burgers is doubled and added to the square of the number of cans of spinach, the total equals 59. When the square of the number of cans of spinach is doubled and added to the square of the number of burgers, the total equals 43. Find the number of burgers and cans of spinach.
How many "mathematical" solutions does this problem have? What is the feasible number of burgers and cans of spinach purchased?
When the guys got home, Olive Oyl (a stingy harridan) nagged them about spending $2.98 per can of spinach and $4.58 per burger (without fries!). With 6% sales tax, what was the total spent?

2b^2+s^2 = 59
2s^2+b^2 = 43
b^2 = 432s^2, so
2(432s^2)+s^2 = 59
3s^2 = 27
s=±3
so, b=±5
Only positive values are "feasible", so
s=3,b=5
(2.98*3 + 4.58*5)*1.06 = 33.75