Name:________________________________________________________________________________Date:_____/_____/__________
1. Solve the following MULTIPLICATION two-step equations:
Remember: Get rid of constant FIRST (zero pairs); then, get rid of coefficient
(divide on both sides)!!
KCC for subtraction!!
3x + 24 = -6
45 = 8x – (-5)
2. Solve the following DIVISION two-step equations:
Remember: Get rid of constant FIRST (zero pairs); then, get rid of FRACTION
(multiply on both sides)!!
KCC for subtraction!!
𝑥
−5
3.
- 3 = -10
25 = 15 +
Solve the following division two-step equations:
BE CAREFUL!! Read the hint in the speech bubble to the right . . .
𝑥+4
=8
−2
𝑥
3
These are different . . .
Multiply on both sides by
the denominator FIRST!
−3+𝑥
=5
4
Two-step Equation
“Speed dating”
Teacher will give directions . . .
Today’s Lesson:
What:
equation word problems
Why:
To use an EQUATION in order to solve
for the unknown in several real-life
situations.
Follow these steps . . .
HOW???
Highlight key information!
Step 1: _________________
Step 2: Identify the MAIN question– this
unknown
will be “x”– the main ______________!
Step 3: Use the “clues” to set up the
equation
_________________!
one-step equation word problems:
1) Last week, Eric ran 8 more miles
than Nick. Eric ran a total of 33 miles.
How many miles did Nick run?
What is the main question (“unknown”)?
Let “x” = _____________________________________________________________
# of miles Nick ran
x + 8 = 33
If Nick is x
then Eric is
x+8 !
x = 25 miles
2) Kaylee collected 14 less cans than
Logan. Kaylee collected 54 cans. How
many cans x did Logan collect?
What is the main question (“unknown”)?
Logan’s # of cans
Let “x” = _____________________________________________________________
x - 14 = 54
If Logan’s
cans are x,
then Kaylee’s
cans are
x - 14 !
x = 68 cans
3) Juan finished three times the amount
of math problems, compared to Maria.
If Juan finished 27 math problems, how
many did Maria finish?
What is the main question (“unknown”)?
# of problems Maria finished
Let “x” = _____________________________________________________________
If Maria’s
problems are
x, then Juan’s
problems are
3x !
3x = 27
x = 9 math problems
4) Mary sold 4 times as many candy
bars as John (for the school fundraiser).
If Mary sold 84 candy bars, how many
candy bars did John sell?
What is the main question (“unknown”)?
Let “x” = _____________________________________________________________
# of bars John sold
4x = 84
If John’s candy
bars are x,
then Mary’s
candy bars are
4x !
x = 21 candy bars
6) Elizabeth won some money in a
contest. She decided to split the money
equally among herself and her two
brothers (what a kind sister). She
receives $73.26, after she split the
money. How much money did she
originally win?
What is the main question (“unknown”)?
amount of $ won
Let “x” = _____________________________________________________________
𝒙
𝟑
If the original $
is x, then this
amount will be
split between 3
people! This is
𝒙
!
𝟑
= 73.26
x = $219.78
Two-step equation word problems:
1) Jane has $575 in her checking
account. She has decided to deposit $85
per month until she has a total of
$1,340. In how many months will this
occur?
What is the main question (“unknown”)?
# of months
Let “x” = _____________________________________________________________
575 + 85x = 1,340
We begin with
$575 in the
account. If x is
the # of months,
then 85x
represents the
total added to
the account!
x = 9 months
2) You have $75 in your checking
account. You are saving for an i-Pad that
costs $500. You will save $25 per month
until you have enough money. How
many months m will this take?
What is the main question (“unknown”)?
Let “m” = _____________________________________________________________
# of months
75 + 25m = 500
We begin with
$75 in the
account. If m is
the # of months,
then 25m
represents the
total added to
the account!
m= 17 months
3) George bought three video games
at the same price. He also bought a DVD
for $20.00. If he spent $65.00 total,
how much was each video game?
What is the main question (“unknown”)?
Let “x” = _____________________________________________________________
cost of each video game
3x + 20 = 65
If the cost of
each video
game is x, then
3x is the cost
for 3 video
games. Don’t
forget the DVD
for $20!
x = $15
Multiple choice:
4) At the basketball game, Will scored
4 points more than two times the # of
points that Hank scored. Will scored 16
points. How many points p did Hank
score?
What is the main question (“unknown”)?
Let “p” = _____________________________________________________________
Hank’s # of points
If Hank’s
points are p,
then (using
the clue)
Will’s points
are . . . !
A)
4 + p² = 16
B)
4 + p = 16
C)
2p + 4 = 16
5) During cross-country season, Kelly
ran five miles more than three times the
# of miles that Michelle ran. Kelly ran
95 miles. How many miles m did
Michelle run?
What is the main question (“unknown”)?
Let “m” = _____________________________________________________________
Michelle’s # of miles
If Michelle’s
miles are m,
then Kelly’s
miles are . . .
A)
3m - 5 = 95
B)
3m + 5 = 95
C)
m + 3(5) = 95
END OF LESSON
The next slides are student copies of the notes for this
lesson, including the HOMEWORK. These notes were
handed out in class and filled-in as the lesson
progressed.
NAME:
Math-7 NOTES
DATE: ______/_______/_______
What: equation word problems
Why: To use an EQUATION in order to solve for the unknown in several real-life
situations.
One-Step Word Problems (write AND solve an equation for each):
HOW???
Step 1: _______________________ key information!!
Step 2: Identify the MAIN question– this will be “x”– the main
__________________________!
Step 3: Use the “clues” to set up an ________________________________ !
GUIDED (Addition Equation)
Let “x” = _______________________________
1) Last week, Eric ran 8 more miles than Nick.
Eric ran a total of 33 miles. How many miles did
Nick run?
What is the main question (“unknown”)?
YOUR TURN (Subtraction Equation):
Let “x” = _______________________________
2) Kaylee collected 14 less cans than Logan.
Kaylee collected 54 cans. How many cans x did
Logan collect?
What is the main question (“unknown”)?
GUIDED (Multiplication Equation):
Let “x” = _______________________________
3) Juan finished three times the amount of math
problems, compared to Maria. If Juan finished 27
math problems, how many did Maria finish?
What is the main question (“unknown”)?
YOUR TURN (Multiplication Equation):
Let “x” = _______________________________
4) Mary sold 4 times as many candy bars as
John (for the school fundraiser). If Mary sold 84
candy bars, how many candy bars did John sell?
What is the main question (“unknown”)?
GUIDED (Division Equation):
5) Elizabeth won some money in a contest. She
decided to split the money equally among herself
and her two brothers (what a kind sister). She
receives $73.26, after she split the money. How
much money did she originally win?
What is the main question (“unknown”)?
Let “x” = _______________________________
Two-Step Word Problems:
GUIDED:
Let “x” = _______________________________
1) Jane has $575 in her checking account. She
has decided to deposit $85 per
month until she has a total of $1,340. In how
many months will this occur?
What is the main question (“unknown”)?
YOUR TURN:
Let “m” = _______________________________
2) You have $75 in your checking account. You
are saving for an i-Pad that costs $500. You
will save $25 per month until you have
enough money. How many months m will
this take?
What is the main question (“unknown”)?
GUIDED:
Let “x” = _______________________________
3) George bought three video games at the
same price. He also bought a DVD for
$20.00. If he spent $65.00 total, how much
was each video game?
What is the main question (“unknown”)?
MULTIPLE CHOICE (choose equation that matches situation):
GUIDED:
4) At the basketball game, Will scored 4 points
more than two times the # of points that
Hank scored. Will scored 16 points. How
many points p did Hank score?
A)
4 + p² = 16
B)
4 + p = 16
C)
2p + 4 = 16
A)
3m - 5 = 95
B)
3m + 5 = 95
C)
m + 3(5) = 95
What is the main question (“unknown”)?
YOUR TURN:
5) During cross-country season, Kelly ran five
miles more than three times the # of miles
that Michelle ran. Kelly ran 95 miles. How
many miles m did Michelle run?
What is the main question (“unknown”)?
NAME:__________________________________________________________________________________ DATE: _____/_____/__________
Math-7 homework
One-Step Word Problems (write AND solve an equation for each):
You may use a
calculator, but
you must show
all steps!!
1) Last week, Bob ran 5 more laps than Sheila. Bob ran a total of 12 laps. How
many laps did Sheila run? (Hint: Use an addition equation to solve)
2) Shannon bought a book for $14.99, but used a coupon to receive a discount.
Her total, after the discount, was $9.99. How much did the coupon save her?
(Hint: Use a subtraction equation to solve)
3) How many bags of chips can you buy with $12.00 if one bag of chips costs
$0.75? (Hint: Use a multiplication equation to solve)
4) You make a batch of homemade cookies that you decided to split equally
among yourself and five of your friends at lunch. If each of you receive three
cookies, how many cookies did you bake to begin with? (Hint: Use a division
equation to solve)
Two-Step Word Problems (write AND solve an equation for each):
1) You already have $225 in your checking account. You would like to save a total
of $550, and have decided to save $65 per month. How many months will this
take?
2) During football season, the Redskins scored a total of three more than three
times the amount of points that the Cowboys scored. The Redskins scored a
total of 336 points in the season. How many points did the Cowboys score?
3) Kiley bought four movie tickets at the same price. She also bought a jumbo
popcorn for $8. If her total was $52, how much did she spend on each movie
ticket?
Multiple Choice:
1) Jack earns $15 a week, plus $3.00 for every
time he washes the dishes without being asked.
Last week, Jack earned $27. Let x represent the
# of times he washed the dishes. Which
equation could be used to solve for x ?
A.
B.
C.
D.
15 + 3 = 27x
15x + 3 = 27
15 + 3x = 27
15 – 3x = 27
2) Olivia’s car uses 3 times as much gas as
Jane’s car uses. If Olivia’s car used 24 gallons of
gas on a trip, which equation could be used to
show how much gas Jane’s car used on the same
trip?
A.
B.
C.
D.
3x = 24
3 + x = 24
24 + 3 = x
24 – x = 3
3) You buy four bracelets that were the same
price each. You also buy a purse for $30. You
spent a total of $40. Which equation could be
used to solve for the amount that each bracelet
costs?
A.
B.
C.
D.
4x – 30 = 40
4x + 40 = 30
30x + 4 = 40
4x + 30 = 40
A.
B.
C.
D.
8 + h = 64
8h = 64
64 – 8 = h
64 + h = 8
4) Leslie gets paid $8 per hour to babysit. If
Leslie got paid $64, which equation could be
used to solve for how many hours, h, Leslie
babysat?
5) Write a situation that matches the
following equation.
40 + 5x = 65