Question

Henry is going on a trip to Brazil. He is currently deciding which cities he will visit during his stay. The table below shows potential cities he could visit, as well as what he estimates it will cost him to visit each one. All costs are given in Brazilian reals (R$).

City
Cost (R$)
Salvador
224
Duque de Caxias
242
Rio de Janeiro
193
Campinas
185
Porto Alegre
153
Guarulhos
120
Fortaleza
201

Henry’s original plan was to visit Duque de Caxias, Campinas, Rio de Janeiro, and Guarulhos. However, he only has R$699 to spend, so he cannot afford to use his original itinerary. Which of the following changes will be the cheapest swap Henry can make and still come in under budget?
a.
Replace Duque de Caxias with Salvador.
b.
Replace Duque de Caxias with Fortaleza.
c.
Replace Rio de Janeiro with Porto Alegre.
d.
Do not visit Guarulhos.

Answer 1

Original plan cost = 242 + 185 + 193 + 120 = R$740, which is R$41 over budget (R$699).

Check each change:
a) Swap Duque de Caxias (242) for Salvador (224): 740 − 242 + 224 = R$722 (still over budget).
b) Swap Duque de Caxias (242) for Fortaleza (201): 740 − 242 + 201 = R$699 (meets budget).
c) Swap Rio de Janeiro (193) for Porto Alegre (153): 740 − 193 + 153 = R$700 (still over budget).
d) Do not visit Guarulhos (remove 120): 740 − 120 = R$620 (under budget, but a larger change).

The cheapest swap that brings him under (or to) budget is b.