Question

Jody's older brother is only three years less than twice Jody's age. If the sum of their ages is 30, then which of the following is the age of Jody's brother?1. 72. 113. 194. 23

Answer 1

`3)19`

Step-by-step explanation

Let Jody's age be j.

Let Jody's brother's age be b.

His brother is three years less than twice his age. This means that:

`b=2j-3`

The sum of their ages is 30. This means that:

`b+j=30_{}`

We now have two simultaneous equations:

`\begin{gathered} b=2j-3 \\ b+j=30 \end{gathered}`

Substitute the first equation into the second equation:

`\begin{gathered} 2j-3+j=30 \\ 3j=30+3=33 \\ j=(33)/(3) \\ j=11 \end{gathered}`

To find b, substitute the value of j into the first equation:

`\begin{gathered} b=2(11)-3=22-3 \\ b=19 \end{gathered}`

That is the age of Jody's brother.