L + 5 = A
L - 4 = J
L + (L + 5) + (L - 4) = 34
Solve for L and then the other ages.
L - 4 = J
L + (L + 5) + (L - 4) = 34
Solve for L and then the other ages.
Let's say Althea's age is A, Leah's age is L, and Jessica's age is J.
We know that Althea is 5 years older than Leah, so we can express this as A = L + 5.
We also know that Leah is 4 years older than Jessica, so we can express this as L = J + 4.
Lastly, we know that the sum of their ages is 34, so we can express this as A + L + J = 34.
We can now use this information to solve for the ages of the individuals.
Substituting the second equation into the first equation, we get A = (J + 4) + 5, which simplifies to A = J + 9.
Substituting these values into the third equation, we get (J + 9) + (J + 4) + J = 34, which simplifies to 3J + 13 = 34.
Now we can solve for J:
3J + 13 = 34
3J = 34 - 13
3J = 21
J = 7
Now that we know Jessica's age is 7, we can substitute this value back into the second equation to find Leah's age:
L = J + 4
L = 7 + 4
L = 11
Finally, we can substitute both values back into the first equation to find Althea's age:
A = L + 5
A = 11 + 5
A = 16
Therefore, Althea is 16 years old.