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Solving Equations & Inequalities
Word Problems
Objectives:
•To solve word problems involving linear equations and
inequalities.
VOCAB OF WORD PROBLEMS
ADDITION
SUBTRACTION
SUM
MORE THAN
PLUS
INCREASED BY
DIFFERENCE
LESS THAN
MINUS
DECREASED BY
MULTIPLICATION
PRODUCT
TIMES
MULTIPLIED BY
PER
DIVISION
QUOTIENT
DIVIDED BY
VOCAB OF WORD PROBLEMS
WORD
IS/ARE
OPERATION
=
IS LESS THAN
IS GREATER THAN
IS LESS THAN OR
EQUAL TO
IS GREATER THAN OR
EQUAL TO
QUANTITY
A NUMBER
OPPOSITE OF A
NUMBER
<
>
≤
≥
( )
X
-X
EXAMPLES
1) Twenty-five is the quotient of a number y
and 3.5.
y
25 
3 .5
2) Three times the quantity two less than a
number x is ten.
3 x  2
  10
3) Twenty-three less than the difference of
thirty-eight and a number n is less than
eight.
(38  n)  23  8
PRACTICE
1) Nine less than the product of ten and a
number d is eleven.
10d  9  11
2) Five increased by eight is four times a
number.
5  8  4x
3) Fifty multiplied by the quantity twenty divided
by a number n is greater than or equal to two
hundred fifty.
 20 
50   250
 n 
EXAMPLES
4) The sum of three numbers is 123. The
second number is 9 less than two times the
first number. The third number is 6 more
than three times the first number. Find the
three numbers.
x
FIRST
NUMBER
SECOND
NUMBER
The second number is 9 less than
two times the first number.
The third number is 6
THIRD more than three times the
NUMBER
first number.
2x  9
3x  6
EXAMPLES
4) The sum of three numbers is 123. The second number is 9
less than two times the first number. The third number is 6
more than three times the first number. Find the three
numbers.
The sum of three numbers is 123.
( x)  (2 x  9)  (3x  6)  123
x  2 x  9  3x  6  123
6 x  3  123
6 x  126
x  21 1st # = 21
2nd # = 2x-9 = 2(21) -9 = 42 – 9 = 33
3rd # = 3x + 6 = 3(21) + 6 = 63 + 6 = 69
EXAMPLES
5) A video store charges $8 to rent a video
game for five days. You must be a member
to rent from the store, but the membership
fee is free. A video game club in town
charges only $3 to rent a game for five
days, but membership in the club is $50 per
year. Which rental plan is more economical?
STORE
RENTAL
FEE

NUMBER
RENTED

CLUB
RENTAL
FEE

NUMBER
RENTED

8  x  3  x  50
8x  3x  50
CLUB
MEMBERSHIP
FEE
EXAMPLES
5) A video store charges $8 to rent a video game for five days.
You must be a member to rent from the store, but the
membership fee is free. A video game club in town charges
only $3 to rent a game for five days, but membership in the
club is $50 per year. Which rental plan is more economical?
If you rent less than 10
video games a year, choose
the Video Store.
If you rent 10 video games
a year choose either one.
8x  3x  50
5x  50
x  10
If you rent more than 10
video games a year, choose
the Video Game Store.
PRACTICE
4) The bill (parts and labor) for the repair of a car
was $458. The cost of parts was $339. The cost
of labor was $34 per hour. Write and solve an
equation to find the number of hours of labor.
5) A rock-climbing gym charges nonmembers $16 per
day to use the gym and $8 per day for equipment
rental. Members pay a yearly fee of $450 for
unlimited climbing and $6 per day for equipment
rental. Write and solve an equation to find how many
times you must use the gym to justify becoming a
member.
PRACTICE
4) The bill (parts and labor) for the repair of a car
was $458. The cost of parts was $339. The cost
of labor was $34 per hour. Write and solve an
equation to find the number of hours of labor.
339  34 x  458
34 x  119
x  3.5 hours of labor
PRACTICE
5) A rock-climbing gym charges nonmembers $16 per day to use
the gym and $8 per day for equipment rental. Members pay a
yearly fee of $450 for unlimited climbing and $6 per day for
equipment rental. Write and solve an equation to find how many
times you must use the gym to justify becoming a member.
16d  8d  450  6d
If you use the gym 25
24d  450  6d times, they will be
equal in price.
18d  450
If you use the gym
d  25
more than 25 times, it
will be worth becoming
a member.