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the answer is there are 225 children in the feeding program.
step by step solution:
to compute for the total number of children at the feeding program, allow x to be the number of children at the feeding program. then, 2/3x will represent those that are 8 years old, 2/5 (x - 2/3x) will represent those that are 9 nine years old. if there are 45 children who are ten years old then, 2/3x + 2/5 (x - 2/3x) + 45 = x. simplify the equation by distributing 2/5 to x - 2/3x thus, 2/3x + 2/5x - 4/15x + 45 = x. combine all the similar terms making it 2/3x + 2/5x - 4/15x - x = -45. find the least common denominator for 1, 3, 5, and 15 thus, 2(5)x + 2(3)x - 4x - 15x/15 = -45. then, 10x + 6x - 4x - 15x/15 = -45. 16x - 19x/15 = -45. multiply both sides of the equation by 15 to eliminate the denominator. 15[-3x/15 = -45]15. -3x = -675. divide both sides of the equation to solve for the value of x then, x = 225. if there were 225 children at the feeding program. 2/3(225) = 450/3 = 150, there are 150 children who are 8 years old. since the number of ten year old kids is given, we can now compute for the number of the 9 year old kids thus, 225 - 150 + 45 = 225 - 195 = 30. therefore, there are 30 children aged 9 at the feeding program.