The sum of the ages of Jose and Valerie is 78 years. 9 years ago, Jose's age was 3 times Valerie's age. How old is Jose now?

(A) Translate the given information into an equation using the variable x = current age of Jose. Your equation should contain 78, 3, and 9. Do not simplify your equation.



(B) How old is Jose currently?
Jose is years old

Jose's age = X yrs.

Valerie's age = Y yrs.
Eq1: X + Y = 78.

9 yrs. ago:
Jose's age: x-9 yrs.
Valerie's age: y-9 yrs.

x-9 = 3(y-9).
x-9 = 3y-27.
Eq2: x - 3y = -18.

Subtract Eq2 from Eq1:
Difference: 4y = 96.
Y = 24 = Valerie's current age.

X + 24 = 78.
X = 54 = Jose's current age.

(A) To translate the given information into an equation, we need to use the information provided.

According to the problem statement, the sum of the ages of Jose and Valerie is 78 years. So, we can set up the equation:

x + y = 78

where x is the current age of Jose and y is the current age of Valerie.

The second piece of information states that 9 years ago, Jose's age was 3 times Valerie's age. We can represent Jose's age 9 years ago as (x - 9) and Valerie's age 9 years ago as (y - 9). So, we can set up another equation:

x - 9 = 3(y - 9)

Combining both equations, we get:

x + y = 78
x - 9 = 3(y - 9)

(B) To find out how old Jose currently is, we need to solve the system of equations.

From the first equation, we can express y in terms of x:

y = 78 - x

Substituting this value of y into the second equation, we can solve for x:

x - 9 = 3((78 - x) - 9)
x - 9 = 3(69 - x)
x - 9 = 207 - 3x
4x = 216
x = 54

Therefore, Jose is currently 54 years old.