Name:
Systems of Equations Word Problems
Write the system of equations. Decide which method to use to solve (Graphing, Substitution, Elimination). Solve the
system, check your work, and define what the solution means in the context of the problem.
Problem
The state fair is a popular field trip
destination. This year the senior class at High
School A and the senior class at High School B
both planned trips there. The senior class at
High School A rented and filled 8 vans and 8
buses with 240 students. High School B rented
and filled 4 vans and 1 bus with 54 students.
Every van had the same number of students in
it as did the buses. Find the number of
students in each van and in each bus.
All 231 students in the Math Club went on a
field trip. Some students rode in vans which
hold 7 students each and some students rode
in buses which hold 25 students each. How
many of each type of vehicle did they use if
there were 15 vehicles total?
Rent-A-Hunk o' Junk charges $29.95 per day
and 43¢ per mile. Tom's Total Wrecks charges
$45 per day plus 32¢ per mile. After how
many miles will they charge the same amount?
Method System of Equations and Solve
Check
Meaning of
solution
Problem
The senior classes at High School A and High
School B planned separate trips to New York
City. The senior class at High School A rented
and filled 1 van and 6 buses with 372 students.
High School B rented and filled 4 vans and 12
buses with 780 students. Each van and each
bus carried the same number of students. How
many students can a van carry? How many
students can a bus carry?
The Anytime long-distance plan charges
$4.80 per month plus $0.05 a minute. The
Talk More plan charges $0.09 a minute
and no monthly fee. For what number of
minutes are the charges for the two plans
the same?
At a high school championship basketball
game 1200 tickets were sold. Student tickets
cost $1.50 each and adult tickets cost $5.00
each. The total revenue collected for the game
was $3200. How many student tickets were
sold? How many adult tickets were sold?
Method System of Equations and Solve
Check
Meaning of
solution
Problem
Car A costs $25,000 to purchase and $0.35 a
mile to drive. Car B costs $18,500 to purchase
and $0.40 a mile to drive. How many miles (x)
would one have to drive before the total cost
(y) of driving Car A and Car B would be the
same?
Brenda's school is selling tickets to a spring
musical. On the first day of ticket sales the
school sold 3 senior citizen tickets and 9 child
tickets for a total of $75. The school took in
$67 on the second day by selling 8 senior
citizen tickets and 5 child tickets. What is the
price of one senior citizen ticket and one child
ticket?
The treasurer of the student body at a college
reported that the receipts from a recent
concert totaled $916. Furthermore, he
announced that 560 people had attended the
concert. Students were charged $1.25 each for
admission to the concert, and adults were
charged $2.25 each. How many adults
attended the concert?
Method System of Equations and Solve
Check
Meaning of
solution
Problem
Kristin spent $131 on shirts. Fancy shirts cost
$28 and plain shirts cost $15. If she bought a
total of 7, then how many of each kind did she
buy?
Let’s-Get-in-Shape Fitness Center has two
different membership plans. Option 1 is a one
time joining fee of $100 and a monthly fee of
$40. Option 2 has no joining fee and a
monthly fee of $60. Write a system of
equations to represent the situation. Graph to
find out after how many months the two plans
will cost the same amount of money.
DeShawn and Shayna are selling flower bulbs
for a school fundraiser. Customers can buy
bags of windflower bulbs and bags of daffodil
bulbs. DeShawn sold 10 bags of windflower
bulbs and 12 bags of daffodil bulbs for a total
of $380. Shayna sold 6 bags of windflower
bulbs and 8 bags of daffodil bulbs for a total of
$244. What is the cost each of one bag of
windflower bulbs and one bag of daffodil
bulbs?
Method System of Equations and Solve
Check
Meaning of
solution