Question

Ryan is nine years younger than two times his friend Peter's age. The sum of theirages is greater than six.What is the youngest age Peter can be? Give your answer as a whole numberThe youngest age Peter can be is years old.

Answer 1

Let be "r" Ryan's age and "p" Peter's age.

According to the information given in the exercise, Ryan is nine years younger than two times his friend Peter's age.

Then, since "two times" indicates multiplication by 2 and "nine years younger" indicates a Subtraction, you can set up the following equation:

`r=2p-9`

You also know that the sum of their ages is greater than six. Then, to represent this you have to use an inequality:

`r+p>6`

The symbol ">" means "Greater than".

Therefore, the procedure to determine the youngest age Peter can be is to substitute the first equation into the inequality and solve for "p"

`\begin{gathered} r+p>6 \\ (2p-9)+p>6 \\ 3p>6+9 \\ 3p>15 \\ \\ p>(15)/(3) \\ p>5 \end{gathered}`

Then, Peter is (at least) 6 years old.

Therefore, the answer is: The youngest age Peter can be is 6 years old.