(a) Let h and d represent the numbers of packages of Hamburger and hotDog buns, respsectively.
.. h +d = 12 . . . . . . . . . . . . the family brought 12 packages of buns
.. 2.00h +1.50d = 20 . . . . each family contributed $20
(b) Double the first equation and subtract the second one
.. 2(h +d) -(2h +1.5d) = 2(12) -(20)
.. 0.5d = 4 . . . . . . . . . . . . . . . . . . . . . simplify
.. d = 8 . . . . . . . . . . . . . . . . . . . . . . . . multiply by 2
.. h = 12 -d = 4
They brought 4 packages of hamburger buns and 8 packages of hotdog buns.
(c) The number of hotdog bun packages cannot exceed 20/1.5 = 13.3 or the budget will be exceeded.
(d) It depends on the relationship of the variables to the ordered pair.
.. (h, d) = (5, 7) would mean 5 hamburger bun packages and 7 hotdog bun packages
.. (d, h) = (5, 7) would mean 7 hamburger bun packages and 5 hotdog bun packages
(e) Their cost for that purchase would be 7*2.00 +4*1.50 = 14.00 +6.00 = 20. That purchase meets the cost constraint, so is fair from a cost contribution point of view. Whether it is fair from a menu point of view depends on the number of hamburgers and hotdogs that need buns.
