5E Systems of Equations Word Problems
Step 1: Define your variables and write the equations
Step 2: Solve the systems of equations by either elimination or substitution
Step 3: Answer the question.
Example 2: Sam bought 3 burritos and 2 tacos for $9. Julie
bought 5 burritos and a taco for $11.50 from the same restaurant.
What would the total cost of 2 tacos and 1 burrito be?
B=Burrito T=Taco
3B + 2T = 9
x(1)
5B + 1T = 11.50
(elimination)
3B + 2T = 9
x(-2)
-10B – 2T = -23
-7B
= -14
B = 2 so 5(2) + 1T = 11.50  T = 1.50
2T + 1B  2(1.50) + 1(2) = $5
1-3: Write (but do not solve) equations for the following situations:
1. Rafael is three times Julie’s age. Their combined ages is 44 years old.
Example 1
There are four times as many cats as dogs.
There are a total of 40 animals. How many cats are there?
D=dogs; C= cats; C=4D
C + D = 40
Substitution
4D + D = 40
5D = 40
D = 8 so C=4(8) = 32 cats
2. Two angles are supplementary (sum up to 180o). The larger angle is five less than twice the smaller angle.
3. Three times the largest of two consecutive odd integers plus the smallest consecutive odd integers is 50.
4-26: Write the equations and solve.
4. Mary is four times John’s age. Their combined ages is 65.
How old is Mary?
8. In one evening, a pizza parlor collected 700 coins for a total
of $145. If the coins are all dimes and quarters, how many of
each kind are there?
5. The length of a rectangle is four times its width. The
perimeter is 80 in. Find the length and the width.
9. The owner of a pet store spent $236 on 10 dogs and cats.
The cats cost $18 each, and the dogs cost $26 each. How
many of each did the owner buy?
6. A 53-inch length of board is cut into two pieces. One piece
is 17 inches longer than twice the other. How long is each
piece?
10. Mr. Miller’s farm and Mr. Newton’s farm together cover
525 acres. Mrs. Miller’s farm is 65 acres larger than Mr.
Newton’s.
Find the size of each farm.
7. The sum of two angles is
Find the angles.
180 . Their difference is 70  .

11. One angle is 10 less than four times the other. If the
angles are supplementary, find the measure of each angle.
12. The perimeter of a rectangle is 36 cm. If the length is
doubled, the perimeter is 60 cm. Find the original length and
width.
19. Tyler is going to the East County Fair and Monique is
going to the West County Fair. The cost to get into the East
County Fair is $5 and $ .50 for each ride. The cost to get into
the West County fair is $3 and $1 for each ride. After how
many rides will they have spent the same amount of money?
13. The sum of two numbers is 30. Their difference is 12.
What are the numbers?
20. BlueJay Cab Company charges a $5 flat fee and $1 per
mile. SafeWay Cab Company charges a $1 flat fee and $3 per
mile. After how many miles will the companies be the same
and how much will it cost?
14. Charles spent $3.70 for 22 stamps. If he bought only 15cent stamps and 20-cent stamps, how many of each did he
buy?
21. Jared and Michaela are climbing stairs of the Empire State
Building. Jared started on the 5th floor and climbs 1 flight of
stairs every minute. Michaela starts on the 2nd floor and
climbs 2 flights a minute. When will they be on the same
floor and what floor will they meet on?
15. A group of people went to a movie together. They spent
$24.75 for 8 tickets. If adult tickets cost $4.50 and children’s
tickets cost $2.25, how many of each kind of ticket were
bought?
16. Mary has 15 coins with a total value of $1.75. If the coins
are nickels and quarters, how many of each kind are there?
22. Geraldine and Jack are saving money. Geraldine starts
with $100 and saves $20 a month. Jack starts with $70 a
month and saves $30 a month. After how many months will
they have saved the same amount of money and how much
will they each have saved?
23. PickMe Cab Company charges a $4 flat fee and $.70 every
half mile. WinSome Cab company charges a $1 flat fee and
$.80 every half mile. After how many miles will the
companies be the same and how much will it cost?
17. Together, Max and Raoul sold 137 tickets for a benefit
baseball game. If Max sold 10 fewer than twice as many as
Raoul, how many tickets did each boy sell?
24. The combined ages of Sally and Tom is 51 years old.
Sally is twice as old as Tom. How old is Sally?
18. Sue paid $46 for 2 adult and 4 child tickets to a play.
Karen paid $86 for 4 adult and 7 child tickets to the same play.
What is the cost of 1 adult and 1 child ticket?
25. A book store sells used books. Paperback books cost
$1.00.Hardback books sell for $5.00.The store sold 100 books
and made $260 from the sale. How many paperback books did
the store sell?
A. $17.00
B. $17.50
C. $18.50 D. $19.00
A. 20
B. 40
C. 60
D. 80