A neighborhood recreation program serves a total of 280 children who are either 11 years old or 12 years old. the sum of the children's ages is 3,238 years. how many 11-year-old children does the recreation program serve?

Answer is: there is 122 children eleven years old.

x - eleven years old children.

y - twelve years old children.

1) x+y = 280, x = 280 - y

2) 11x+12y = 3238.

put x from 1) equation into 2):

11· (280-y) + 12y = 3238.

3080 - 11y + 12y = 3238.

y = 158.

x = 280 - 158 = 122.

The total number of students = 280

Sum of ages of children = 3238

Let the number of children of ages 11 year old = x

and the number of children of ages 12 year old = y

Equation 1. x+y=280

Equation 2. 11x + 12y = 3238

From Equation1. y = 280-x

Now, put the value of Y in equation 2 which gives 11x+12 (280-x) = 3238

from this, 11x + 3360-12x = 3238

x = 3360-3238

x = 122 = children of age 11 years.

putting value of x in equation 1,

122+y = 280

y = 280-122

y = 158 = children of age 12 years

Answer. children of age 11 years = 122