Download Systems of Equations – Word Problems – Notes

Algebra 1-1 DA
Name_______________________________________
Ch. 5 Applications of Linear Systems Homework
Write a system of linear equations for each situation. Solve using substitution or elimination. Make sure
that you answer the question.
1. The sum of two numbers is 21. The larger number is 6
less than twice the smaller number. Find the two numbers.
2. The difference of two numbers is 15. The larger number
is 1 more than 3 times the smaller number. Find the two
numbers.
3. William is 3 years older than Charmaine. The sum of 3
times Charmaine’s age and 2 times William’s age is 76.
How old are William and Charmaine?
4. Alysha is two years younger than Bryce. The sum of
their ages is 28. How old is Alysha?
5. Tyshon’s age is 3 less than three times Cedric’s age.
The sum of their ages is 57. How old is Tyshon?
6. The sum of their ages is 97. The difference of their ages
is 19. Find their ages.
7. Tickets to the concert were $2.50 for adults and $1 for students. $1200 was collected and 750 tickets were sold.
Write a system of linear equations that can be used to find how many adults (a) and how many students (b) attended.
How many students attended?
System of equations:
Answer ______________________________
8. Abby filled her goodie bags with 4 cookies and 3 candy bars and spent a total of $10.25 per bag. Marissa filled her
goodie bags with 2 cookies and 7 candy bars and spent a total of $14.75 per bag. Each cookie costs the same amount.
Each candy bar costs the same amount. Write a system of linear equations that can be used to find the cost of one cookie
(x) and one candy bar (y). What was the cost, in dollars, of each candy bar?
System of equations:
Answer ______________________________
9. Christian sold tickets to game. Good seats were $5 each and poor seats cost $2 each. 210 people attended and paid
$660. Write a system of linear equations that can be used to find how many good seats (g) and how poor seats (p) were
sold. How many of each type of seat were sold?
System of equations:
Answer ______________________________
10. Gerard bought 9 hamburgers and 3 orders of fries for $24.75. Chris bought 6 hamburgers and 4 orders of fries for
$19.50. Each hamburger costs the same amount. Each order of fries costs the same amount. Write a system of linear
equations that can be used to find how much one hamburger (h) cost and one order of fries (f) cost. What is the cost, in
dollars, for each item?
System of equations:
Answer ______________________________