Question

there are 125 sixth graders in Euclid Middle School. Each is either 10 or11 years old. The median age is 0.48 years greater than the mean age. How many 10 years old students are in the group?

Answer 1

Okay i got a solution

Answer 2

since there are 125 sixth graders (odd number) the median can only be either 10 or 11.
We will continue solving with 2 options, in the end one will be rejected, since there can only be one answer.

Thus mean age, we also have 2 options, either 10- .48 = 9.52 or 11-.48 = 10.52

Now, let the number of 10 yrs old kid in x and 11 yrs old kid be y

We can form 2 eqn, x+y = 125 ---(1)
and \[\left( 10x+11y \right)/(x+y)\] ---- (2)

rearrange (1), x= 125-y , substitute into (2)
\[[10\left( 125-y \right)+11y]/ 125 = 9.52 or 10.52\]
1250 -10 y + 11y = 1190 or 1315
y= 1190- 1250 or 1315- 1250
y= -65 or 60 (-65 is rejected cause y cannot be negative)

y= 60

Solving for x,

x+y= 125
x+60=125
x= 65

Answer 3

Thank you