Writing Equations with Variables on Both Sides

Blind company A charges $25.00 to install blinds for one room and $5.00 for each additional window. Blind company B charges $30.00 to install blinds in one room and $4.00 for each additional window. Write an equation to determine how many blinds would need to be installed for the price to be equal.

• 25 + 5x = 30 + 4x
• 25 - 5x = 30 - 4x
• 30 - 25 = 4x + 5x
• 25x + 5 = 30x + 4

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CCSS.6.EE.B.6

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CCSS.6.EE.A.4

Carol wants to join a dance studio. Studio A charges $100.00 for the entry fee and $45.00 per class, while Studio B charges $125.00 for the entry fee and $30.00 per class.  Write an equation to determine how many classes would need to be taken for the price to be equal? 

• 125 - 100 = 45x + 30x
• 100x + 45 = 125x + 30
• 100 + 45x = 125 + 30x
• 100 - 45x = 125 - 30x 

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CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.EE.C.9

A rental car agency charges $30.00 per day plus per mile $0.15. Another rental car agency charges $36.00 per day plus $0.10 per mile. Which equation could be used to determine how many miles would have to be driven in one day for both rental agencies to cost the same amount to rent? 

• 30 + 0.15x = 36 + 0.10x
• 30 - 0.15x = 36 - 0.10x
• 30 + 36 = 0.10x + 0.36x
• 36 - 30 = 0.36x + 0.10x

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CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.EE.C.9

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At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal? 

• 150x + 24 = 180 + 20x
• 150 + 24x = 180 + 20x
• 180 - 150 = 24 x + 20x
• 150 - 24x = 180 - 20x

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CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.EE.C.9

Mary has been offered two jobs. Job A has a starting salary of $36,000 and a raise of $1500 every year. Job B has a starting salary of $29,000 and a raise of $2500 every year. Write an equation to determine how many years would Mary's salary be the same at both companies. 

• 36,000x + 1,500 = 29,000x + 2,500
• 36,000 - 29,000 = 1,500x + 2,500x
• 36,000 - 1,500x = 29,000 - 2,500x
• 36,000 + 1,500x = 29,000 + 2,500x

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CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.EE.C.9

CCSS.6.EE.A.4

I can join video club A for $25.00 and rent videos for $1.00 each. Or, I can join video club B for $15.00 and rent videos for $2.00 each. Write an equation that could be used to determine how many rentals would be needed for the price to be equal.

• 25 - x = 15 - 2x
• 25 + 15 = x + 2x
• 25x + 1 = 15x + 2
• 25 + x = 15 + 2x

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CCSS.6.EE.B.6

CCSS.6.EE.B.7

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value? 

• 15x + 2.5 = 10x + 3
• 15 - 2.5x = 10 - 3x
• 15 + 2.5x = 10 + 3x
• 15 - 10 = 2.5x + 3x

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CCSS.6.EE.B.6

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CCSS.6.EE.A.2

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Erin weighs 135 pounds and is gaining 1/2 pound each week. Miranda weighs 143 pounds and is losing 1/4 pound each week. Which of the following equations could be used to determine x, the number of weeks that it will take until the two girls weigh the same amount?

• 135 + 1/2x = 143 + 1/4x

• 135 + 1/2x = 143 - 1/4x

• 135x + 1/2 = 143x + 1/4

• 135 - 1/2x = 143 + 1/4x

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CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.EE.C.9

Mike is driving a boat at 12 mph and is increasing his speed by 0.2 mph each second. Hank is driving a boat at 25 mph and is decreasing his speed by 0.7 mph each second. Which of the following equations could be used to determine x, the number of seconds it will take for the boats to be traveling the same speed?

• 12x + 0.2 = 25x - 0.7

• 12 - 0.2x = 25 + 0.7x

• 12.2x = -25.7x

• 12 + 0.2x = 25 - 0.7x

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CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.EE.C.9

CCSS.6.EE.B.5

CCSS.6.EE.A.4

Renting a kayak costs $10 per hour. Renting a canoe costs $5 per hour plus a $7 fee. Which equation could be used to determine h, the number of hours for which they each cost the same? 

• 10h=5h+7
• 10h=5+7h
• 10h+5h=7
• 5h=10h+7

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CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.EE.B.5