Help with this maths question?

You wish to make the lowest possible average from the other 4, so that it will counteract a high value for the 5th, to bring the average down to 150.4 once they are included.

If Minimum weight = 130, assume 1 student is 130

Then assume the other 3 are exactly 5 pounds apart, the lowest combination

130, 135, 140, 145

The mean of these 4 numbers and the weight of the heaviest, must be 150.4 pounds

130+135+140+145 = 550

=> (550 + x)/5 = 150.4

=> 550 + x = 752

=> x = 202 pounds.

and to check, find the mean of 130, 135, 140, 145, 202

= 752/5 = 150.4

The catch on this one is "no two students weights are within 5 pounds of each other". What units can we use? Can they be within 5.00000000000000001 lbs of each other or do we have to round up to 6 pounds or can we used 10ths of a pound at 5.1? Did the book specify?? It will make a difference in the answer.

I'm going to guess the book will allow them to be 5 lbs apart (which is incorrect since they can't be "within" 5 lbs of each other), so

We'll say your heaviest student weighs x pounds. Your 4 lightest students are 130, 135, 140 & 145 lbs. The mean is the total weight divided by number of students. So we get

(130 + 135 + 140 + 145 + x)/5 = 150.4

(550 + x)/5 = 150.4

550 + x = 150.4 * 5 = 752

x = 752 - 550 = 202, that is the heaviest a student can be

The total mass is 150.4*5=752 lb

If we have 4 light students the other must be heavier than otherwise

The lightest student well shall assume is 130 lb

The others at intervals of 5 lb 135 lb 140lb and 145 lb repetitively.

So the heavy student ways 752 - 130 - 135 - 140 -145 = 202 lb