When on vacation, a traveler calculated his non-hotel daily expenses

Question

When on vacation, a traveler calculated his non-hotel daily expenses as follows: on a frugal day he could spend as little as $35, on an average day he would spend $50, and on a splurge day he would spend a minimum of $75. If the traveler has at most $300 for a 5 day trip, what is the maximum number of splurge days he could have?

A. 1
B. 2
C. 3
D. 4
E. 5

A. 1
B. 2
C. 3
D. 4
E. 5

mohshu · Answer

if all the days are splurge,,,
frugal = 0
normal = 0

then max splurge days = 4

ans D

mohshu · Answer

as per the stem, it says,, 5 day trip.. if all the days are splurge,, we can have 4 days trip only with 300$
hence next highest number is 3 days splurge plus 2 day frugal
total 295.. well within 300 as the stem says atmost 300

ans C

Ze3rebz · Answer

The information gives us the following two equations:

75x + 35y= 300
x + y=5

x is the splurge days 
y is the frugal days

We only use the frugal days rate instead of the normal rate to maximise the number of splurge days.
X= 3.125 = 3

Answer is C

steffe440 · Answer

Let s be the number of splurge days, then the remaining days after splurge days are 5 - s

Hence we have

75s + 35(5-s)  ≤ 300

75s + 175 - 35s ≤ 300

40s ≤ 125

s ≤ 3.125

Alternative way of thinking:

If we want to maximize splurge we have to minimize the days when he does not splurge, and since he needs to survive 5 days it is quite obvious he cannot splurge every day.

Hence we have 75 + 75 + 75 =225, if we splurge another day we do not have enough money for the last day.

hence he can only splurge 3 times without running out of money the last two days, hence a max of 3 splurge days is possible.

When on vacation, a traveler calculated his non-hotel daily expenses

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When on vacation, a traveler calculated his non-hotel daily expenses

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