Name: ______________________
Common Core Algebra
Linear Word Problems & Consecutive Integers Practice
1. The sum of 4 less than 3 times a number and the number increased by 10 is 14. What is the
number?
2. Frank is 5 less than twice Michelle’s age. Casey is 1 more than three times Michelle’s age. If
Frank and Casey’s ages add up to 51, then how old is Michelle?
3. The sum of two numbers is 21. One number is three less than the other. What is the larger of
the two numbers?
4. Mike is currently 35 years older than his daughter. In three years, Mike will be five more than
four times his daughter’s age. How old are both of them now?
5. There is a contest at the local fair to guess the age of the four employees working the table.
Amber is six years less than Debbie’s age. Bonnie is two years more than half of Debbie’s age.
Charlie is two years more than Debbie’s age. If the sum of all of their ages is 96, then how old is
the youngest person? Who is the youngest person?
6. Find two consecutive integers where three times the smaller of the two integers is twelve more
than twice the larger integer.
7. Find three consecutive odd integers where three times the smallest integer is one less than
twice the largest integer.
8. Three consecutive even integers are such that the sum of the smallest and three times the
second is 38 more than twice the third. Find the integers.
9. Allie, Ben, and Cat were born in consecutive years. Allie being the youngest and Cat the oldest.
The sum of Allie and Ben’s ages is ten less than three times Cat’s age. How old will Ben be in five
years?
10. The sum of five consecutive integers is 0. Find the smallest of these integers.