Question

Joe, Sam, and Chris are all brothers. Joe is 5 years older than Chris, and Sam is three × as old as Chris. The sum of their ages is 20. How old is Sam?

a) Sam is 7 years old.
b) Sam is 8 years old.
c) Sam is 9 years old.
d) Sam is 10 years old.

Answer 1

The problem is solved by setting up an equation based on the given information about ages and solving for Chris's age. Multiplying Chris's age by 3 gives us Sam's age, which is 9 years old.

Step-by-step explanation:

The question asked is a mathematical problem involving linear equations. To find out how old Sam is, we need to define variables for each person's age based on the information given and set up equations accordingly. Let's denote Chris's age as c. According to the problem, Joe is 5 years older than Chris, so Joe's age will be c + 5. Sam is three times as old as Chris, making Sam's age 3c. Given that the sum of their ages is 20, we can write an equation summarizing the information:

c + (c + 5) + 3c = 20

Combining like terms in the equation we get:

5c + 5 = 20

To find c, we will solve the equation:

5c = 20 - 5

5c = 15

c = 3

Now that we have Chris's age, we can determine Sam's age by multiplying c by 3:

Sam's age (3c) = 3 × 3 = 9

Therefore, Sam is 9 years old, which corresponds to option (c).