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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 Translate the following into an equation. Eighteen is 6 less than four times a number 18 = 4n – 6

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

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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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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

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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? m = months to save $1800 – total goal $825 – in his account $65 – deposit per month 2) Write an equation. 65m + 825 = 1800

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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. 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

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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 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

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

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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 = 300B) x + 60 = 300 C) 60x + 16 = 300D) 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 2) Write an equation. 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 2) Write an equation. 2h+ 4 = 10

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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 = 128B) 2x - 12 = 128 C) 2x + 12 = 128D) x - 12 = 128

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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 = 128B) 2x - 12 = 128 C) 2x + 12 = 128D) 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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M IX F REEZE P AIR S HARE #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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M IX F REEZE P AIR S HARE #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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M IX F REEZE P AIR S HARE #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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M IX F REEZE P AIR S HARE #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

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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.

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M IX F REEZE P AIR S HARE #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

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M IX F REEZE P AIR S HARE #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.

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