Question

Ron is five years older than twice his cousin Pats age. The sum of their ages is less than 35.What is the greatest age that Pat can be.A) 7B)8C)9D)10

Answer 1

Data:

• Ron is 5 years older than twice his cousin Pat's age.

,

• The sum of their ages is less than 35

Procedure

1. We will assign variables to the parameters to build the equation.

• Ron's age: R

,

• Pat's age: P

2. Analyzing the description:

`R=2P+5`

The latter equation means that Ron is 5 years older than twice the age of his cousin.

Based on the information, we can build a second equation:

`R+P<35`

This means that the sum of their ages is less than 35.

To get the greatest age that Pat can be, we have to replace one equation in the other. For that, we have to isolate the first equation for R.

`R=2P+5`

Then, we will replace the latter on the second equation:

`2P+5+P<35`
`3P<35-5`
`3P<30`
`P<10`

However, the interval is telling us that number 10 is not included. Thus, the next number would be 9. If we try the latter equations, we can see that 9 meets both conditions:

`R=2\cdot9+5=23`
`23+9<35`

Answer: C) 9