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Verified Answer :

apologiabiology

consecutive interegers are 1 apart
they are x,x+1,x+2
sum is 126
x+x+1+x+2=126
3x+3=126
minus 3 both sides
3x=123
divide both sides by 3
x=41
x+1=42
x+2=43

the ages are 41,42,43

Lampa20

lets set up variables

x - elsa ages
y - edna ages
z - ellie ages

From the text we can write equations
y = x+1
z = y+1
because each after elsa is 1 year older than previous of them.

now we write equation
x + y + z = 126 
and express our equations above in this one:
x + x + 1 + x + 2 = 126
3x = 123
x = 41

that means that elsa is 41 years old, edna 42 years old and ellie 43 years old.