Four years ago, twice Athena's age was five less than her cousin's age. At present, the age of Athena's cousin is 18 years less than thrice Athena's age. What are their ages now?
If Athena's age 4 years ago is x, then her cousin's age 4 years ago is what? Is it that her cousin is older?
Athena's age is expressed as a function of the cousin's age, so it is usually easier to define the domain
Four years ago:
let the cousin's age be x
then Athena was 2x-5
present:
cousin ---- x+4
Athena ----- 2x-5 + 4 or 2x - 1
x+4 = 3(2x-1) - 18
x+4 = 6x - 3 - 18
25 = 5x
x = 5
subbing into my definitions:
the cousin is now 9 and Athena is now 9
mmmhhh, let's check this
4 years ago, Athena was 5 and the cousin was 5
Twice Athena's age would be 10, and 5 less would be 5, which is the cousin's age.
Now, three times Athena's age is 27 , less 18 is 9, which is the present age of the cousin
My answers are correct
Posting an Answer
Yes, if Athena's age 4 years ago is represented by x, then her cousin's age 4 years ago would be greater than x because the problem states that twice Athena's age 4 years ago was five less than her cousin's age. This implies that Athena's cousin is older than Athena.
Let's solve this step by step:
Step 1: Define the variables
Let x be Athena's age 4 years ago.
Let y be her cousin's age 4 years ago.
Step 2: Translate the problem
From the problem statement, we can write two equations:
Equation 1: 2x = y - 5 (Twice Athena's age 4 years ago was five less than her cousin's age)
Equation 2: y = 3(x + 4) - 18 (The age of Athena's cousin is 18 years less than thrice Athena's age)
Step 3: Solve the system of equations
Let's substitute Equation 1 into Equation 2:
2x = 3(x + 4) - 18
Expanding and combining terms:
2x = 3x + 12 - 18
Simplifying:
2x = 3x - 6
Subtracting 2x from both sides:
0 = x - 6
Adding 6 to both sides:
6 = x
Therefore, Athena's age 4 years ago is 6.
Substituting this value into Equation 1:
2(6) = y - 5
Expanding and simplifying:
12 = y - 5
Adding 5 to both sides:
y = 17
Therefore, Athena's cousin's age 4 years ago was 17.
Step 4: Calculate their current ages
To find their current ages, we need to add 4 years to their ages 4 years ago.
Athena's current age = x + 4 = 6 + 4 = 10 years old
Cousin's current age = y + 4 = 17 + 4 = 21 years old
So, Athena's current age is 10 years old, and her cousin's current age is 21 years old.