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
Now:
Valeries age --- x
Jose's age ------ 78-x
9 years ago:
Val ----- x-9
Jo ------ 78-x-9 = 69-x
at that time Jose was 3 times as old as Val
69-x = 3(x-9)
solve for x
(A) To solve this problem, let's set up the equations using the given information:
Let x be the current age of Jose.
Let y be the current age of Valerie.
We are given two pieces of information:
1) The sum of their ages is 78: x + y = 78.
2) Nine years ago, Jose's age was 3 times Valerie's age: (x - 9) = 3(y - 9).
(B) To find Jose's current age, we need to solve the equations simultaneously. Let's solve for x.
From equation 2, we can simplify it as: x - 9 = 3y - 27.
Rearranging and simplifying further, we get: x - 3y = -18.
Now we have a system of equations:
x + y = 78
x - 3y = -18
To solve this system, we can use the method of substitution or elimination.
Using the substitution method, we can solve for x by isolating y in equation 1 and substituting it into equation 2:
From equation 1, we get y = 78 - x.
Substituting y in equation 2, we have:
x - 3(78 - x) = -18.
Expanding and simplifying, we get:
x - 234 + 3x = -18.
Combining like terms, we have:
4x - 234 = -18.
Adding 234 to both sides:
4x = 216.
Dividing by 4, we get:
x = 54.
Therefore, Jose is currently 54 years old.
(B) Jose is 54 years old.