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Please help me solve the following SAT Math question: I know the answer but I don't understand how to solve it so please explain the problem as you solve it.

For the numbers r, s, and t, the average (arithmetic mean) is twice the median. If r<s<t, r=0, and t=ns, what is the value of n?

By Star448 (Star448) on Saturday, October 04, 2003 - 08:45 pm: Edit

say the average of r, s, and t is a. since r is 0, it doesn't count as a number, so you can just say (s + t)/2=a. the median would also have to be s, since it's the middle highest, so 2s=a. now you can combine the equations, so (s+t)/2=2s, then s+t=4s, then 3s=t. since ns=t, n would be 3, i think.

By Student9 (Student9) on Saturday, October 04, 2003 - 08:55 pm: Edit

let's assign values.

there are three numbers so let's make their sum equal to a multiple of three.

(0 + s + t)/3 = 2(s)
(s + t) = 6(s)
t=5(s)
ns=5s
n=5

for proof:
r=0
s=4
t=20
n=5

I think this is correct.

By Chrisy (Chrisy) on Saturday, October 04, 2003 - 09:05 pm: Edit

student 9 is correct.
my steps:
(r+s+t)/3=2s
(0+s+ns)/3=2s
factor out the s:
s(n+1)/3=2s
multiply 3 on both sides:
s(n+1)=6s
divid by s:
n+1=6
n=5