Problem Solving

[vladmire]

How do I figure out the total cost?

The total cost of the vacation was divided equally among 3 people. If the total cost of the vaction had been divided equally among 4 people, the cost per person would ahve been $50 less. What was the total cost of the vaction?

$200

$300

$400

$500

$600

[hwiya320]

x = total cost (constant)
y = cost per person when divided by 3 people

x/3 = y or x = 3y

x/4 = y-50
when total cost (x) is divided by 4 people = y (cost per person) - $50

substitute first equation

3y/4 = y-50 (move the 4 now)
3y = 4(y-50)
3y = 4y - 200
-y = -200
y = 200 per person originally

so 200 x 3 people = 600 total cost.

to verify your answer, 600/4 = 150, 50 dollars less than original cost.

[Stuart@KaplanGMAT]

How do I figure out the total cost?

The total cost of the vacation was divided equally among 3 people. If the total cost of the vaction had been divided equally among 4 people, the cost per person would ahve been $50 less. What was the total cost of the vaction?

$200

$300

$400

$500

$600

By far the easiest way is to backsolve from the answers.

let's quickly eliminate (A), (C) and (D), because they're not divisble by 3.

Now we can try either $300 or $600. Let's try $300:

300/3 = 100 each
300/4 = 75 each

Not $50 difference, eliminate (B)... only one answer left, choose (E).

Almost 0 algebra, very quick solution!

[hwiya320]

I hate you Stuart...




no, I just admire your knowledge...

[Deepak_J_Shah]

Total cost = x
From the question,
x/4 = x/3-50
> x/4-x/3 = -50
=>3x-4x = 12*(-50)
=> x = 600