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 + = 31 EXAMPLE #2 Translate the following into an equation Eighteen is less than four times a number 18 = 4n – EXAMPLE #3 Translate the following into an equation The quotient of a number and 5, increased by 8, is equal to 14 n + = 14 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 MINI QUICK CHECK #1 ANSWERS Translate the following phrases to equations 1) Three more than four times a number is 23 4x + = 23 2) Four less than twice a number is 2x – = 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 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 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 we know? b = boxes of cards  – handling charge  – cost per box of cards  26 – total cost  2) Write an equation 3b + = 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 + = 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 we know? c = Cole’s age  37 – total ages (the sum)  years older than Cole – Lawrence’s age  2) Write an equation 2c + = 37 EXAMPLE #10 – SUMMER OLYMPICS In the 2000 Summer Olympics, The United States won more medals than Russia Together they won 185 medals Write an equation to find how many medals Russia won 1) What we know? R = Russia’s medals  185 – total medals (together)  more medals than Russia – US won  2) Write an equation 2R + = 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 we know? h = Larry’s homeruns  10 – total homeruns (together)  more than twice Larry – Andre’s homeruns  2) Write an equation 2h+ = 10 MINI QUICK CHECK #3 1) Todd is 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 inches taller than his brother The sum of their heights is 139 inches Write an equation to find his brother’s height 2x + = 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 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 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 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   x + 12 = 65 ... 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 to Ms Ruark and then shared the rest with five... 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 A furniture rental store charges a down-payment of $100 and... 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