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

9 yrs. ago:

Valerie's age = X yrs.
Jose' age = 3x yrs.

The present:
Valerie: (x+9) yrs. old.
Jose: (3x+9) yrs. old.

x+9 + 3x+9 = 78.
4x + 18 = 78.
4x = 60.
X = 15 yrs.

3x+9 = 3*15 + 9 = 54 yrs. = Jose's age.

thank you

is the equation going to be

x+9+3x+9=78

Glad I could help.

A) To translate the given information into an equation, let's assume the current age of Jose is x. We are given that the sum of the ages of Jose and Valerie is 78 years. So, the current age of Valerie can be expressed as 78 - x.

9 years ago, Jose's age was 3 times Valerie's age. So, Jose's age 9 years ago was x - 9, and Valerie's age 9 years ago was 78 - x - 9.

According to the given information, Jose's age 9 years ago was 3 times Valerie's age 9 years ago. We can write this as:

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

Simplifying the equation, we get:

x - 9 = 3(69 - x)

B) To find out how old Jose is currently, we need to solve this equation for x.

First, distribute the 3 on the right side of the equation:

x - 9 = 207 - 3x

Now, let's gather the x terms on one side and the constant terms on the other side:

x + 3x = 207 + 9

Combining like terms:

4x = 216

Finally, divide both sides of the equation by 4 to solve for x:

x = 54

Therefore, Jose is currently 54 years old.

So, the answer to part B is:

Jose is 54 years old.