Althea is 5 years older than Leah, and Leah is 4 years older than Jessica. The sum of thier ages is 34. How old is Althea?
L + 5 = A
L - 4 = J
L + (L + 5) + (L - 4) = 34
Solve for L and then the other ages.
althea=16
To find out how old Althea is, we need to go step by step. Let's assign variables to the ages of the three individuals.
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.