1. Writing System of Equations
Algebra 1
Writing
System of Equations

2. Systems of Equations Writing Equations
STEP 1: Read problem.
STEP 2: Identify variables and label them.
STEP 3: Re-read problem, writing as you go.
STEP 4: Double- check your answer.
Does it make sense?

3. Example #1 Mr. Frankel bought 8 tickets to a puppet show and
spent $30. He bought a combination of child tickets
for $3 each and adult tickets for $5 each. Which
system of equations will determine the number of
adult tickets, a, and the number of child tickets, c, he
bought?
a = number of adult tickets
c = number of child tickets
Tickets: a + c = 8
Money: 5a + 3c = 30

4. Example #2 Ms. Rechtin purchased 12 boxes containing a total
of 70 golf balls. She bought a combination of
small boxes, each containing 3 golf balls, and large
boxes, each containing 20 golf balls. Which system
of equations will determine the number of small
boxes, s, and the number of large boxes, l, she
bought?
s = number of small golf balls
l = number of large golf balls
Golf balls: s + l = 12
Boxes: 3s + 20l = 70

5. Example #3 Sam visits the Cookie Store and
spends a total of $6.40. Raisin cookies
sell for 30cents each and chocolate
chip cookies sell for 25cents each. He
buys 3 more raisin cookies than
chocolate chip cookies. Which system
of equations best represents the
situation if C represents the number of
chocolate chip cookies and R the
number of raisin cookies?
C = number of chocolate chip cookies
R = number of raisin cookies
Money: 0.30R C = 6.40
Cookies: R = C + 3

6. Example #4
Sally buys 12 tickets to the Fun-Time Circus for a total of $58. If
adult tickets cost $6.00 each and child tickets cost $2.50 each,
which System of equations best represents the situation? A
represents the number of adult tickets bought and C the number
of children tickets bought.
A = number of adult tickets
C = number of child tickets
Money: 6A C = 58
Tickets: A + C = 12

7. Example # 5 Jason went to the Hamburger Shack twice last
week. On the first trip he bought 3 hamburgers
and 4 orders of french fries for $7.10. On the
second trip he bought only 2 hamburgers and an
order of french fries for $3.40. Which system of
equations best represents this situation if H
represents the cost of each hamburger purchased
and F the cost of each order of French fries?
H = Cost of a hamburger
F = Cost of each order of French fries
3H + 4F = 7.10
2H + F = 3.40

8. Example # 6 Logan went to the cafeteria twice last week. On
Monday he had 2 hot dogs and a carton of milk
totaling $ On Wednesday he had 3 hot dogs
and 2 cartons of milk totaling $4.45. Which
system of equations best represents the situation
if H represents the cost of each hot dog and M
represents the cost for each carton of milk?
M = cost of a carton of milk
H = cost of a hotdog
2H + M = 2.85
3H + 22M = 4.45

9. EXAMPLE #7 The Delicious Ice Cream Shop sells sundaes for $2.00 and
bananas splits for $3.00. On a hot summer day the shop
sold 7 more sundaes than banana splits and made $110.
Which system of equations could be used to find the
number of sundaes, s, and banana splits, b, that the shop
sold that day?
s = number of sundaes
b = number of banana splits
2s + 3b = 110
s = b + 7

10. EXAMPLE #8 The length of a rectangular pool is twelve feet more
than the width. The perimeter of the pool is 120 feet.
Which system of equations can be used to find the
pool’s length and width?
l = length of a rectangle
w = width of a rectangle
l = w + 12
2l + 2w = 120