Writing Two-Step Equations with quick checks

MINI QUICK CHECK #1Translate the following phrases to equations... 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

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TRANSLATING TWO-STEP

EQUATIONS

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EXAMPLE #1

Translate the following into an equation

Seven more than three times a number is 31

3x + 7 = 31

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EXAMPLE #2

Eighteen is 6 less than four times a number

18 = 4n – 6

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EXAMPLE #3

The quotient of a number and 5, increased by

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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

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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

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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?

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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

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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

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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

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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

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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

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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

2R + 9 = 185

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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

2h+ 4 = 10

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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

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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

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M IX F REEZE P AIR S HARE

#1

The difference between four times a number and 10 is 22

4x – 10 = 22

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#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

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#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

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#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

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#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

(x – 3) ÷5 = 10 OR x = 5(10) +3

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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.

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Hilde rented the table

550

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#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.

65

12 2

1

= +

x

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