Writing Two-Step Equations with quick checks

TRANSLATING
TWO-STEP
EQUATIONS


EXAMPLE #1
Translate the following into an equation.
Seven more than three times a number is 31

3x + 7 = 31


EXAMPLE #2
Translate the following into an equation.
Eighteen is 6 less than four times a number

18 = 4n – 6


EXAMPLE #3
Translate the following into an equation.
The quotient of a number and 5, increased by
8, is equal to 14

n
+ 8 = 14
5


MINI QUICK CHECK #1
Translate the following phrases to

equations.
1) Three more than four times a
number is 23
2)Four less than twice a number
is 2


MINI QUICK CHECK #1
ANSWERS
Translate the following phrases to
equations.
1) Three more than four times a
number is 23
4x + 3 = 23
2) Four less than twice a number is 2
2x – 4 = 2


EXAMPLE #4 – VERIZON WIRELESS
You can call anyone outside of Verizon for
$.20 per minute plus a monthly fee of $9.99.
1) Define the variable
n = number of minutes
2) Write an expression
.20n + 9.99
3) Suppose your monthly bill was $54.60.
Write an equation to find how many minutes
you used to call outside of Verizon.
.20n + 9.99 = 54.60

EXAMPLE #5 – BANK ACCOUNT
John had $825 in his savings account. He has
decided to deposit $65 per month until he
has a total of $1800. Write an equation to
help John find out how many months he has
to save until he has a total of $1800 saved.
1) What do we know?
m = months to save
 $1800 – total goal
 $825 – in his account
 $65 – deposit per month


2) Write an equation.
65m + 825 = 1800


EXAMPLE #6 – TEMPERATURE
Suppose the current temperature is 17ºF. It is
expected to rise 3ºF each hour for the next
several hours. Write an equation to
determine how many hours it will take for the
temperature to be 32ºF.
1) What do we know?
h = hours
 32ºF – final temperature
 17ºF – current temperature
 3ºF – temperature increase each hour


2) Write an equation.
17 + 3h = 32


EXAMPLE #7 – GREETING CARDS
A mail-order greeting card company charges
$3 for each box of greeting cards plus a
handling charge of $2 per order. Write an
equation to find out how many boxes of cards
you can order from this company if you want
to spend $26?
1) What do we know?
b = boxes of cards
 2 – handling charge
 3 – cost per box of cards
 26 – total cost


2) Write an equation.
3b + 2 = 26


MINI QUICK CHECK #2
1) The temperature is 8ºF. It is expected
to rise 5ºF each hour for the next
several hours. Write an equation to
determine how many hours the
temperature will rise until it is 48ºF
outside.

2) A carpet store advertises 16 square
yards of carpeting for $300, which
includes the installation charge of
$60. Which equation could be used to
determine the cost of one square
yard of carpet?
A) 16x = 300
B) x + 60 = 300
C) 60x + 16 = 300
D) 16x + 60 =
300


MINI QUICK CHECK #2
ANSWERS

1) The temperature is 8ºF. It is expected
to rise 5ºF each hour for the next
several hours. Write an equation to
determine how many hours the
temperature will rise until it is 48ºF
outside.
5h + 8 = 48
2) A carpet store advertises 16 square
yards of carpeting for $300, which
includes the installation charge of
$60. Which equation could be used to
determine the cost of one square
yard of carpet?
A) 16x = 300

B) x + 60 = 300
C) 60x + 16 = 300
D) 16x + 60
= 300


EXAMPLE #9 – AGES
Lawrence is five years older than his brother
Cole. The sum of their ages is 37. Write an
equation to find out how old Cole is.
1) What do we know?
c = Cole’s age
 37 – total ages (the sum)
 5 years older than Cole – Lawrence’s age


2) Write an equation.
2c + 5 = 37


EXAMPLE #10 – SUMMER OLYMPICS
In the 2000 Summer Olympics, The United
States won 9 more medals than Russia.
Together they won 185 medals. Write an
equation to find how many medals Russia
won.
1) What do we know?
R = Russia’s medals
 185 – total medals (together)
 9 more medals than Russia – US won



2) Write an equation.
2R + 9 = 185


EXAMPLE #11 – BASEBALL
HOMERUNS
Andre hit four more homeruns than twice the
number of homeruns Larry hit, h. Together
they hit 10 homeruns. Write an equation to
find how many homeruns Andre hit.
1) What do we know?
h = Larry’s homeruns
 10 – total homeruns (together)
 4 more than twice Larry – Andre’s homeruns


2) Write an equation.
2h+ 4 = 10


MINI QUICK CHECK #3
1) Todd is 5 inches taller than his
brother. The sum of their heights is
139 inches. Write an equation to
find his brother’s height.
2) In a canned food drive, Sam
collected 12 more cans than
Louise. Together, they collected

128 cans. How many cans did Sam
collect?
A) x + 12 = 128
B) 2x - 12 =
128
C) 2x + 12 = 128
D) x - 12 =
128


MINI QUICK CHECK #3
ANSWERS

1) Todd is 5 inches taller than his
brother. The sum of their heights is
139 inches. Write an equation to
find his brother’s height.
2x + 5 = 139

2) In a canned food drive, Sam
collected 12 more cans than
Louise. Together, they collected
128 cans. How many cans did Sam
collect?
A) x + 12 = 128 B) 2x - 12 = 128
C) 2x + 12 = 128 D) x - 12 = 128


MIX FREEZE PAIR SHARE
#1

The difference between four
times a number and 10 is 22

4x – 10 = 22


MIX FREEZE PAIR SHARE
#2
Twelve-year old Aaron O’Leary
of Columbus, Ohio, bought old
bikes at an auction for $350. He
fixed them and sold them for
$50 each. Write an equation to
find how many bikes Aaron
bought to make a $6200 profit.
50b – 350 =
6200


MIX FREEZE PAIR SHARE
#3
There were 640 gallons of water
in a 1600-gallon pool. Water is
being pumped into the pool at a
rate of 320 gallons per hour.
Write an equation to find how
many hours it will take to fill
the pool.
320h + 640 =
1600

MIX FREEZE PAIR SHARE
#4
Mandy bought a DVD player.
The sales clerk says that if she
pays $80 now, her monthly
payments will be $32 per
month. Write an equation to
find how many months Mandy
will have to pay if the total cost
is $400.
80 + 32m = 400


MIX FREEZE PAIR SHARE
#5
Marla brought a bag of candy
to school with x pieces in it.
She gave 3 to Ms. Ruark and
then shared the rest with five
of her friends. If each of her
friends ended up with 10
pieces of candy, how much
candy did she start with?
 

(x – 3) ÷5 = 10 OR x = 5(10) +3

MINI QUICK CHECK #4
1.

A furniture rental store charges a
down-payment of $100 and $75 per
month for a table. Hilde paid $550 to
rent the table. Write an equation to
find the number of months Hilde
rented the table.

2.

Jeremy sold half of his baseball cards
to Jacob and then went to the mall
and bought 12 more. He now has 65
baseball cards in his collection. Write
an equation to find out how many
baseball cards Jeremy started with.


MIX FREEZE PAIR SHARE
#6
A furniture rental store
charges a down-payment of
$100 and $75 per month for a
table. Hilde paid $550 to rent
the table. Write an equation to
find the number of months
Hilde rented the table.
 

75m + 100 =
550


MIX FREEZE PAIR SHARE
#7
Jeremy sold half of his baseball
cards to Jacob and then went
to the mall and bought 12
more. He now has 65 baseball
cards in his collection. Write an
equation to find out how many
baseball cards Jeremy started
with.
 

1
x + 12 = 65
2