# Systems of equations word problems

```Name__________________________________________________ Date_______________
Linear Systems Word Problems Summative Assessment
Choose any 4 problems to complete out of #1-5.
1) A museum sells adult tickets for \$6 and child tickets for \$4. In one day the museum
collected \$1590 from 321 people from admissions. How many adults and children were
Define variables:
Equations:
Solve:
2) Suppose you invest \$10,410 in equipment to manufacture a new board game. Each game
costs \$2.65 to manufacture and sells for \$20 How many board games must you make and
Define variables:
Solve:
Equations:
Name__________________________________________________ Date_______________
Linear Systems Word Problems Summative Assessment
3) Castel and Gabriella are selling pies for a school fundraiser. Customers can buy apple pies
and lemon meringue pies. Castel sold 6 apple pies and 4 lemon meringue pies for a total of
\$80. Gabriella sold 6 apple pies and 5 lemon meringue pies for a total of \$94. What is the
cost each of one apple pie and one lemon meringue pie?
Define variables:
Equations:
Solve:
4) The sum of two numbers is 31. Twice the larger number is 7 more than 3 times the smaller
number. What are the numbers?
Define variables:
Solve:
Equations:
Name__________________________________________________ Date_______________
Linear Systems Word Problems Summative Assessment
5) A coin collector has 31 dimes and nickels with a total value of \$2.40. How many of each
coin does he have?
Define variables:
Solve:
Equations:
Name__________________________________________________ Date_______________
Linear Systems Word Problems Summative Assessment
In Questions 6-9. Define the variables, write the equations that represent
the equation, choose a method to solve the system, and explain why. Do
not solve. Choose any 3 out of 4 problems to complete.
6) Your math teacher tells you that next week’s test is worth 100 points and contains 38
problems. Each problem is worth either 5 points or 2 points. How many 5-point questions
are there and how many 2- point questions are there?
Define variables:
Equations:
Which method would you use to solve the system, substitution or elimination, and
why?
7) Producing a musical cost \$88,000 plus \$5900 per performance. One sold-out performance
earns \$7500 in revenue. If every performance sells out, how many performances are needed
to break even?
Define variables:
Equations:
Which method would you use to solve the system, substitution or elimination, and
why?
Name__________________________________________________ Date_______________
Linear Systems Word Problems Summative Assessment
8) Kayla's school is selling tickets to the annual dance competition. On the first day of ticket
sales the school sold 3 senior citizen tickets and 5 child tickets for a total of \$70. The school
took in \$216 on the second day by selling 12 senior citizen tickets and 12 child tickets. Find
the price of a senior citizen ticket and the price of a child ticket.
Define variables:
Equations:
Which method would you use to solve the system, substitution or elimination, and why?
9) The sum of two numbers is 21. The larger number is 6 less than twice the smaller number.
Find the two numbers
Define variables:
Equations:
Which method would you use to solve the system, substitution or elimination, and why?
```