Solving Age Problems with Equations and Graphs

Maria is 3 years older than her brother Tom. If the sum of their ages is 25, what are their ages? Identify the variables and constants in this problem.

• Tom is 12 years old and Maria is 15 years old.

• Tom is 10 years old and Maria is 13 years old.

• Tom is 9 years old and Maria is 12 years old.

• Tom is 11 years old and Maria is 14 years old.

Alicia is twice as old as her sister Jenna. If the sum of their ages is 30, how old is each sister? Graph the equations representing their ages.

• Alicia is 25 years old and Jenna is 5 years old.

• Alicia is 20 years old and Jenna is 10 years old.

• Alicia is 15 years old and Jenna is 15 years old.

• Alicia is 30 years old and Jenna is 0 years old.

John is 5 years older than his friend Mike. If the total of their ages is 40, determine their ages and identify the variables used.

• Mike is 15 years old and John is 20 years old.

• Mike is 17.5 years old and John is 22.5 years old.

• Mike is 10 years old and John is 15 years old.

• Mike is 20 years old and John is 25 years old.

Samantha is 4 years younger than her cousin Alex. If Alex is 20 years old, how old is Samantha? Write the equation and identify the constants.

• 22

• 18

• 16

• 14

Liam and Noah are siblings. If Liam is 2 years older than Noah and their combined age is 34, how old are they? Graph the system of equations that represents their ages.

• Liam is 22 years old and Noah is 12 years old.

• Liam is 18 years old and Noah is 16 years old.

• Liam is 20 years old and Noah is 14 years old.

• Liam is 15 years old and Noah is 17 years old.

Emma is 6 years older than her friend Olivia. If the sum of their ages is 42, find their ages and identify the variables in the equation.

• Olivia is 18 years old and Emma is 24 years old.

• Olivia is 22 years old and Emma is 28 years old.

• Olivia is 15 years old and Emma is 21 years old.

• Olivia is 20 years old and Emma is 26 years old.

Sophia is 8 years younger than her mother. If the mother is 36 years old, how old is Sophia? Write the equation and identify the constants involved.

• 28

• 26

• 34

• 30

Ethan is 10 years older than his sister Mia. If the total of their ages is 50, determine their ages and graph the equations that represent their ages.

• Mia is 20 years old and Ethan is 30 years old.

• Mia is 15 years old and Ethan is 25 years old.

• Mia is 30 years old and Ethan is 40 years old.

• Mia is 25 years old and Ethan is 35 years old.

Isabella is 7 years older than her brother Lucas. If the sum of their ages is 29, what are their ages? Identify the variables and constants in this scenario.

• Lucas is 11 years old and Isabella is 18 years old.

• Lucas is 9 years old and Isabella is 16 years old.

• Lucas is 10 years old and Isabella is 17 years old.

• Lucas is 12 years old and Isabella is 19 years old.

A group of friends consists of two pairs of siblings. If the older sibling in each pair is 3 years older than the younger one, and the total age of all four friends is 50, find their ages and graph the equations.

• 9, 12, 11, 14

• 8, 11, 10, 13

• 7, 10, 9, 12

• Ages are 10, 13, 12, and 15.