Question

PLEASE ANSWER WITH ALL THE MATH

Currently, Jacob’s mother is three more than nine times as old as Jacob. In eleven years, his mother will be five more than three times his age. Write a system of linear equations that models this situation. Let j represent Jacob's age, and let m represent his mother's age.
Write an equation that relates Jacob and his mother's current ages. Solve the system of equations.
What are their ages?

Answer 1

9514 1404 393

Answer:

• Jacob: 4
• his mother: 39

Explanation:

Let J and M represent the current ages of Jacob and his Mother.

currently:

M = 3 +9J

in 11 years:

M+11 = 5 +3(J+11)

Using the first equation to substitute for M in the second, we have ...

(3 +9J) +11 = 5 +3(J +11) . . . . . substitute for M

9J +14 = 3J +38 . . . . . . simplify

6J + 24 . . . . . . . . . . subtract 3J+14

J = 4 . . . . . . . . . . divide by 6

M = 3 +9(4) = 39

Jacob is 4 and his mother is 39.