Problem Solving

Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

a. 78

b. 77 1/5

c. 66 1/7

d. 55 1/7

e. 52

[spoiler]Answer: A. Does anyone know the best method to solve this?[/spoiler]

sum of 5 numbers = 55*5 = 275
median=55
smallest=a,largest=3a+20
range = 2a+20.
for max range, a should be max.
also let other 2 numbers be b,c
4a + 20 + b+ c = 220
4a + b+c = 200
b min can be a and c min can be 55.
4a+a+55=200 or 5a = 145
a=29
range=2a+20 = 78

When you see the word avg you should set up the formula Avg = sum/number

we know that avg is 55 and there are 5 numbers so 55 = Sum/5 which means the sum is 275.

Then we learn that the median = avg - set up 5 lines because median means to put the numbers in order:

___ + ____ + 55 ____ + ____ = 275

then we find that the largest is 20 more than 3 times the smallest so we know:

s + ___ + 55 + ___ + 3s+20 = 275

Then we are trying to find the largest range, which means we want the smallest numbers for the rest of the spaces:

s + s+ 55 + 55 + 3s + 20 = 275

solve to find that s = 29

Then figure out the largest number -- 3(29)+ 20 = 107. The range is the largest minus the smallest:

107 - 29 = 78