To celebrate a colleague's retirement, the T coworkers in an office agreed to share equally the cost of a catered lunch. If the lunch costs a total of x dollars and S of the coworkers fail to pay their share, which of the following represents the additional amount, in dollars, that each of the remaining coworkers would have to contribute so that the cost of the lunch is completely paid?
a) x/T
b) x/(T - S)
c) Sx/(T - S)
d) Sx/T(T - S)
e) x(T - S)/T
I know this problem can be solved with algebra, but I wanted to try and do it picking smart numbers. Unfortunately, the first few sets of numbers I picked gave me both A & D as possible answers. What am I doing wrong when picking smart numbers? Here's an example:
T=10
X=20
S=5
So, originally each person had to pay $2. Since five people didn't pay, the remaining people must pay an extra $2 each. If I plug into A, I get:
T/S = 2
And if I plug into D, I get:
Sx/T(T-S)
100/10(5)
= 2
-------
Here's another set I tried:
T=10
X=20
S=5
So, originally each person was to pay $2 each. Since 5 people failed to pay, the remaining people have to pay $ 4 each, or an extra $2/pp.
Putting the aforementioned numbers in answer A:
T/S = 10/5 = 2
And putting it into D:
Sx/T(T-S)
100/50
= 2
I picked several sets of numbers and it kept coming out the same before I finally found a set that only worked for D. On the real test, I wouldn't have time to fool around with several sets of numbers, so I'm wondering what I can do differently to pick smart numbers?
a) x/T
b) x/(T - S)
c) Sx/(T - S)
d) Sx/T(T - S)
e) x(T - S)/T
I know this problem can be solved with algebra, but I wanted to try and do it picking smart numbers. Unfortunately, the first few sets of numbers I picked gave me both A & D as possible answers. What am I doing wrong when picking smart numbers? Here's an example:
T=10
X=20
S=5
So, originally each person had to pay $2. Since five people didn't pay, the remaining people must pay an extra $2 each. If I plug into A, I get:
T/S = 2
And if I plug into D, I get:
Sx/T(T-S)
100/10(5)
= 2
-------
Here's another set I tried:
T=10
X=20
S=5
So, originally each person was to pay $2 each. Since 5 people failed to pay, the remaining people have to pay $ 4 each, or an extra $2/pp.
Putting the aforementioned numbers in answer A:
T/S = 10/5 = 2
And putting it into D:
Sx/T(T-S)
100/50
= 2
I picked several sets of numbers and it kept coming out the same before I finally found a set that only worked for D. On the real test, I wouldn't have time to fool around with several sets of numbers, so I'm wondering what I can do differently to pick smart numbers?
