Question

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.

Part 1: Write a system of linear equations that models this situation. Let j represent Jacob's age, and let m represent his mother's age.

Part 2:Solve the system of equations
Part 3:complete the sentence.
Jacob isyears old and his mother is years old.

Answer 1

m=3+9j

(m+11)=5+3(j+11)

Jacob is 4 and his mother is 39

Step-by-step explanation:

Answer 2

Part 1: The linear equations are
`m=3+9j` and
`3j-m+27=0`

Part 2: Solving the equations, we have,
`j=4` and
`m=40`

Part 3: Jacob is 4 years old and his mother is 40 years old.

Step-by-step explanation:

Part 1: Let j represent Jacob's age, and let m represent his mother's age.

It is given that, "Jacob's mother is three more than nine times as old as Jacob". Writing it as linear equation, we have,

`m=3+9j`

It is also given that, "In eleven years, his mother will be five more than three times his age". Writing it as linear equation, we have,

`(m+11)=5+3(j+11)`

Simplifying this, we get,

`m+11=5+3j+33\\m+11=3j+38`

Thus, the linear equation is

`3j-m+27=0`

The linear equations are
`m=3+9j` and
`3j-m+27=0`

Part 2: Solving the linear equation, we get,

Substituting
`m=3+9j` in
`3j-m+27=0`

`3j-3-9j+27=0\\`

Simplifying, we get,

`-6j=-24`

Hence,
`j=4`

Substituting
`j=4` in
`m=3+9j`

`m=3+9(4)\\m=3+36\\m=40`

Solving the equations, we have,
`j=4` and
`m=40`

Part 3: Since, j represents jacob and m represents the jacob's mother

Thus, Jacob is 4 years old and his mother is 40 years old.