SOLUTION: 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 3238 years. How many 11 year old chi

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Question 490157: 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 3238 years. How many 11 year old children does the recreation program serve?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
11 year old x children
12 year old y children
.
x+y = 280
11x+12y=3238
1 x + 1 y = 280 .............1
11 x + 12 y = 3238 .............2
Eliminate y
multiply (1)by -12
Multiply (2) by 1
-12 x -12 y = -3360
11 x 12 y = 3238
Add the two equations
-1 x = -122
/ -1
x = 122 ----- 11 year old children
plug value of x in (1)
1 x + 1 y = 280
122 + 1 y = 280
1 y = 280 -122
1 y = 158
y = 158 ---- 12 year old children