# Three Variable Word Problems

1.
2𝑥 + 2𝑥
4𝑦 =
+ 3𝑧
4𝑦
6 −=3𝑧6 Get variables
− 𝑧2𝑦−+
𝑥+
2𝑦𝑧 = −5 on the same
𝑥𝑥−−3𝑦
2𝑧 −=2𝑧
3𝑦=−−7
7 side &amp; line up
x, y, and z
2𝑥 + 4𝑦 + 3𝑧 = 6
1.(-1)( 𝑥 − 2𝑦 + 𝑧 )= −5(-1)
(-2)(𝑥 − 3𝑦 − 2𝑧 )= −7(-2)
-x + 2y – z = 5
x – 3y – 2z = -7
-y – 3z = -2
2x + 4y + 3z =6
-2x + 6y + 4z = 14
10y + 7z = 20
(10)( −𝑦 − 3𝑧 )= −2 (10)
1.
10𝑦 + 7𝑧 = 20
-10y – 30z = -20 10y + 7(0) = 20
10y + 7z = 20
10y = 20
-23z = 0
y=2
z=0
x – 2(0) = 3(2) – 7
x–0=6–7
x = -1
(-1, 2, 0)
Thurs
10/22
Learning Objective:
To solve word problems
with systems
Lesson Hw: Lesson 3 – 5 Word
3–5
Problems WS
Algebra II

To solve word problems using
systems of equations
1. Find the value of two numbers if
their sum is 19 and their difference
is 3.
x + y = 19
11 + y = 19
x–y=3
y=8
2x = 22
x = 11
{8, 11}
2. On the first day of choir ticket sales,
12 adults and 1 student ticket sold for a
total of \$171. Choir took in \$138 on the
second day be selling 6 adult tickets and
4 student tickets. Find the price of an
(-4)12x + y = 171(-4)
6x + 4y = 138
12(13) + y = 171
156 + y = 171
y = 15
-48x - 4y =-684
6x + 4y = 138
-42x = -546
x = 13
\$15 for student tix
3. Jacob sold 14 banana pies and 13
strawberry pies for a total of \$241.
Kim sold 2 banana pies and 6
strawberry pies for a total of \$80.
What is the cost of each pie?
14x + 13y = 241
14x + 13y = 241
-14x
-42y
=
-560
2x
+
6y
=
80
(-7)
(-7)
-29y = -319
2x + 6(11) = 80
y = 11
2x + 66 = 80
\$7 for banana pie
2x = 14
\$11 for strawberry
x=7
4. The sum of three numbers is 6. The
third number is the sum of the first
and second number. The first number
is one more than the third number.
Find the numbers.
x = 1st #
y = 2nd #
z = 3rd #
x+y+z=6
z=x+y
x=z+1
x+y+z=6
x+y–z=0
x
-z=1
4.(-1)x + y + z = 6 (-1)
x+y–z=0
x
-z=1
-x - y - z = -6
x+y–z=0
-2z = -6
z=3
{4, -1, 3}
x–3=1
x=4
4+y+3=6
7+y=6
y = -1
5. Anna is training for a triathlon. In her
training routine each week, she runs 7
times as far as she swims and she bikes
3 times as far as she runs. One week,
she trained a total of 232 miles. How far
did she run that week?
x = swim
y = run
x + y + z = 232
y = 7x
z = 3y
z = bike
x + y + z = 232
-7x + y
=0
-3y + z = 0
x + y + z = 232
-7x + y
=0
(-1)
-3y + z = 0 (-1)
5.
x + y + z = 232 (-4)-7x + y = 0 (-4)
3y – z = 0
x + 4y = 232
x + 4y = 232
28x -4 y = 0
x + 4y = 232
29x = 232
x=8
5. y=7(8)
y = 56
z = 3(56)
z = 168
Swim 8 miles
Run 56 miles
Bike 168 miles
6. Sports Chalet sold 10 gloves, 3 bats,
and 2 bases for \$99 on Monday. On
Tuesday, it sold 4 gloves, 8 bats, and 2
bases for \$78. On Wednesday, it sold 2
gloves, 3 bats, and 1 base for \$33.60.
What are the prices of each item?
x = glove
y = bat
10x + 3y + 2z = 99
4x + 8y + 2z = 78
2x + 3y + z = 33.60
z = base
10x + 3y + 2z = 99
(-1) 4x + 8y + 2z = 78 (-1)
(-2) 2x + 3y + z = 33.60 (-2)
6.
10x + 3y + 2z = 99
-4x – 8y – 2z = -78
6x – 5y = 21
10x + 3y + 2z = 99
-4x – 6y – 2z = -67.2
6x – 3y = 31.8
Glove \$8
Bat \$5.40
Base \$1.40
6.(-1)6x – 5y = 21 (-1)
6x – 3y = 31.8
6x – 3(5.4) = 31.8
-6x + 5y = -21
6x – 16.2 = 31.8
6x – 3y = 31.8
6x = 48
2y = 10.8
x=8
y = 5.4
4(8) + 8(5.4) + 2z = 78
32 + 43.2 + 2z = 78
75.2 + 2z = 78
z = 1.4
7. The sum of three numbers is -4,
The second number decreased by the
third number is equal to the first. The
sum of the first and second number is
-6. What are the numbers?
x = 1st #
y = 2nd #
z = 3rd #
x + y + z = -4
y–z=x
x + y = -6
x + y + z = -4
-x + y – z = 0
x +y
= -6
7.
x + y + z = -4
-x + y – z = 0
x +y
= -6
x + y + z = -4
-x + y – z = 0
2y = -4
y = -2
{-4, -2, 2}
x + (-2) = -6
x = -4
-4 + (-2) + z = -4
-6 + z = -4
z=2
8. The difference of two number is
2. Their sum if 20. What are the
numbers?
x + y = 20
11 + y = 20
x–y=2
y=9
2x = 22
x = 11
{9, 11}
 LAHS
scored 37 points in a
football game. Six points are
award for each touchdown. After
each touchdown, the team can
earn one point for the extra kick,
or two points for a 2-point
conversion. The team scored one
fewer 2-point conversions than
extra kicks. The team scored 10
times during the game. How many