Question

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 1

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.

Answer 2

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